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  1. 1

    Making a lesson plan that utilizes technology

    I'm in need of making a lesson plan that utilizes technology. I can't find any good ideas. Checked out TI and NCTM's websites, to no avail. Anyone have any cool ideas or websites that would work? The lesson plan needs to use technology by means of Excel or a TI calculator.
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    Divisibility Questions

    Two questions here. I know the definitions, but cannot formulate a through proof. 1.a and b are positive integers. If a^3 | (is divisible by) b^2, then a | (is divisible by) b. Now, by definition, I know that a^3*k=b^2, for some k. Also, I know that a * j = b for some j. But where do...
  3. 1

    Finding the pattern

    Is there anyone who can help me? I need to find a pattern in these numbers: 1/2, 1/6, 1/12, 1/20, 1/30, 1/42, 1/56. Now, I know just by looking at the denominators, if I could only work with those, I could use the formula: 2n+a_n_1. But I have that fraction, so it's all screwy. Anyone see...
  4. 1

    Product notation

    I have a quick question. In my book, there is a question that says to express each of the following products in terms of \prod_{n=1}^\k\a{i}, where k is constant. Now, my question is this: \prod_{n=1}^\k\ka_i. Would i just pull the k out becuase it is only a constant and move that to in...
  5. 1

    Quick question regarding Fermat

    I have a question regarding mods and Fermat's Little Theorem. I know Fermat's little theorem states that a^p-1 congruent to 1 (mod p). Also, i know that for every interger a we have that a^p congruent to a (mod p). So, my question is: What is the answer for 3^302 (mod 5)? Would it be 3^301...
  6. 1

    Pythagorean Triples

    Prove that every Pythagorean triple is of the form 3k, 4k, 5k. Could I say that 3k = x = 2st, 4k = y = t^2-s^2, and 5k = z = t^2 + s^2? those are the definitions of the pythagorean triple correct? can anyone say yea or nay? if nay, how can i make it correct?
  7. 1

    Proving with GCD and LCM

    Let a, b, and c be positive integers. I need to prove two items... 1. abc = GCD(a,b,c) * LCM(ab,bc,ac) 2. abc = GCD(ab,ac,bc) * LCM(a,b,c) where the GCD is the Greatest Common Divisor and the LCM is the Least Common Multiple. Could I go ahead and say that (a,b,c)=1, that...
  8. 1

    Fundamental Thm of Arithemetic

    Wow, it has been awhile! China has been fun, but now it is time to get back to the states and also math work! Here is a problem that has been giving me some problems. It reads: \prod from i=1 to n, pi^ai for each i is the canonical representation of a, deduce a formula for the sum of...
  9. 1

    Future Teacher

    I am an aspiring secondary mathematics teacher here in the states. what i want to know is are there any posts/discussions on things that deal with the classroom? i am putting this post here, since this is HW help K-12. can anyone tell me? also, does anyone here belong to NCTM (National...
  10. 1

    Please help, almost finished

    i just can't finish up these proofs but i have my ideas written down on the bottom. also, i have what i think is right written down, but it IS A LOT of stuff to type. can anyone point me in the correct direction to go? i need to show that if gcd(a,n)=(a-1,n)=1, then 1+a+...+a^0 mod n...
  11. 1

    Modulos raised to phi

    hi, it's me again, i only have 3 tiny questions then i am done asking, i hope! i need to show that if gcd(a,n)=(a-1,n)=1, then 1+a+a^2...+a^\phi^n^-^1\equiv0 mod n show (m,n)=1 then m^\phi^n+n^\phi^m\equiv 1 mod (mn) show if m and k are positive integers then \phi(^k)=m^k-1\phi(m)...
  12. 1

    Palindromes and modulos

    suppose x=(bn,bn-1...b2,b1,b0)base b . show that x is divisible by (b-1)is divisible by the summation of bi, i=0 up to n. (i wish i could find out how to write it in the notation that you guys use on here) also, i need to show that every bsae 7 palindrome interger w/ an even number of...
  13. 1

    Mods that will rack your brain

    show that a^13 is congruent to a (modulo 2730) if a is an integer such that a is not divisidble by 3, or such that a IS divisible by 9, then a^7 is congruent to a (mod 63) with these, could i just divide the mod numbers by the powers? that is what i am doing, but it seems like as though...
  14. 1

    Reduced residue system mod 7

    i need help understanding modulos. i have no grasp on the information and i am wondering if you people can help me. i need to show that the number 3, 3^2, 3^3, up to 3^6 form a reduced residue system mod 7. also, i need help with this... if p and q are distinct prime,s, prove p^q + p^p...
  15. 1

    Lcm and gcd

    i have this one ? and it is bugging me !! show that a,b,c = to (ab,ac,bc)[a,b,c]. () = to the gcd and [] = to the lcm. does that notation mean multiply the numbers together? i mean i started out saying this... (ab,ac,bc) = 1, so there exist a p prime s.t. p divides ab, p divides ac, and p...
  16. 1

    Please help almost done with them

    i have two ?'s to ask yall. ok, i need to prove every even perfect number is a triangular number. the formula is t(n)= 1+2+... tn = (n(n+1))/2. ok i know that to be a perfect number, it is sigma (a) which menas 2times a. for ex, sigma(6)=1+2+3+6=12. this is as far as i can get can anyone...
  17. 1

    Perfect numbers/residue

    ok i like posting on here becuase a. people help me! and b. i have to know my stuff for people to help me. so, i have two ?'s to ask yall. ok, i need to prove every even perfect number is a triangular number. the formula is t(n)= 1+2+... tn = (n(n+1))/2. ok i know that to be a perfect...
  18. 1

    How many positive integers are not divisble by 12 or 15?

    hi i am new to THIS place here but i do put posts on the number theory site as well. i am in need of direction and have no idea where to turn. i need help w/ two ?'s and they are... how many pos int. <1000 are NOT divisible by 12 or 15? prove the if the sum of two consec. int. is a...
  19. 1

    Modulo and congruencies in class

    i am learning about modulo and congruencies in class and i am seeking some help. i need to find a complete residue system mod 11 consisting of odds only. show that every pos int. n, 7^n congruent to 1+6n (mod36) find the least residue of (n-)! mod n for several values of n. find a...
  20. 1

    Seeking direction

    hello all. i am in dire need of direction here and i really appreciate all this help. how many 0's are in 1100! prove tuv=(tu,tv,uv)[t,u,v] only prime that makes 4p+1 a perfect square is p=2. can anyone please help me? i am in so much need of direction... :confused: :cry:
  21. 1

    New member = lotsa ?'s

    i know i've only been on for couple of months, but i was always afraid of asking for help. thanks to this site, i now understand all of this theory stuff! ?'s prove that [alpha] + [alpha + 1/3] + [alpha + 2/3] = [3 alpha] for all reals alpha. prove [alpha] + [beta] <= [alpha +...
  22. 1

    Prove to me that the pythagorean triples

    prove to me that the pythagorean triples are from the form 3k,4k,or 5k. for k >=1. proof: cases for 3K: 3k ^2 9k^2 factor out 3k 3k(3k) 3k+1 ^2 9k^2+1 3k(3k)+1 3k+2 ^2 9k^2+1+3...
  23. 1

    Prove [ac,bc] = to c[a,b]

    hey check out this ?. with c>0, prove [ac,bc] = to c[a,b]. so far, i am saying that c/a and c/b. so, after that i get stuck. any help?
  24. 1

    Some more brain exercises!

    hey i have more problems that can really exercise the mind! here are 3. 1. prove if q is divisible by (r +s) then either q is divisible by r or q is divisible by s. 2. if d>0, (fd+ed) = d(f,e). proof. 3. a divisible by b => a^m divisible by b^m a,b,m are in Z+. i think i have...
  25. 1

    Oh i love these brain exercises!

    if x and y are pos. int. then rx >=y. x is an int. help!
  26. 1

    Inquisitive minds

    if a number is a cube and a square the only forms will be 9k or 9k+1. any suggestions as to how to vaidate this?? would the 8 cases work? from 9k to 9k+8? what does everyone else think? yet another... 10 divides z if and only if (10,z) does not = 1.
  27. 1

    Tables in -5

    i am curious as to how this would look. i wonder how the addition tables would look in base -5? would the multiplication look the same? here is what i know so far: addition multiplication 0 1 2 3 4...
  28. 1

    In need of direction

    i need some help here. i need to show that x=2k+1 and y=9k+4. i need to show that x and y are relatively prime. i am thinking of setting one = to k, and then substitiuting that into the otehr formula. any other suggestions?
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