Recent content by .d9n.

Hi there i was thinking about trying to build a light hovercraft that can transport one person and I had a few questions about the propellers and motors and how they work. The first question is, is it possible to run a hovercraft with an enclosed fan, for example like that found in a jet ski...

i assume this only works if the number of villages is even. Let i=1,2,... then when we have 2i villages we have 3i roads. I can see that when you go alternatively left and right you end up at the start point, I am just not sure why/ can't prove it.

Homework Statement In a certain area there are n villages linked by a network of roads in such a way that exactly three roads meet in each village, and none of the roads meet between villages. Prove that if someone starts in one village and moves round this road system alternately...

its the bit where i get to a<=3, I am not sure what this is meant to be telling me

this is what i haveWe are looking for solutions of: 2^x + 3^y = z^2 [1] where x, y, and z are non-negative integers. So z^2 ≡1 (mod 3) unless z^2=3m for any integer m, and if x is odd, say x=(2k+1) for some integer k. However when z=3, we have 2^3+3^0=3^2, so one solution is when...

Homework Statement what does this equation tell me 2^a=3^b-1? Homework Equations The Attempt at a Solution its meant to be telling me something but I am not sure what

oh so does that mean that x has to be even, is that how i prove it?

if i was right with assuming 2^(2k+1)=2(mod3) then no when x is odd it doesn't agree with z^2

so z^2 =1 (mod3) unless z=3m for any integer m with 2^x im not sure whether 2=1(mod3) or 2=2(mod3) assuming 2=2(mod 3) when x is odd then 2^(2k+1)=2(mod3) and when x is even 2^x=1(mod 3) so I am not too sure where to go from here

Homework Statement i want to prove that x is even in this equation 2^x+3^y=z^2 (1) Homework Equations The Attempt at a Solution what i have so far is (1) is congruent to mod3 2^x=z^2(mod3) when z=1 and x=2 then 4=1(mod3) so therefore x is even? have i proved that x is...

so by two multiplications do you mean a^2 x a^2 so for the qu you mean a^25000 x a^25000 x ... x a^25000 - 40 times say n=1000000 is this what you mean a^1000000=a^500000 x a^500000 =a^ (a^25000)^20 x (a^25000)^20 = (a^25000)^40 or a^2^500000= a^2^2^250000 = a^2^2^2^125000 =...

Homework Statement Given integers a and n, where n > 0, how many multiplications are needed to calculate a^n? You are not expected to produce a precise answer, but if n is a million it should become clear from your answer that 40 multiplications will suffice. Homework Equations...

this is what i have so far, but think i may have gone wrong somewhere, any ideas?We are looking for solutions of: 2^x + 3^y = z^2 [1] where x, y, and z are non-negative integers. We can see that [1] is a congruence modulo 8: 3^y = z^2 (mod 8) [2] When z=1 and and y=2...

so far i have 2^x + 3^y = z^2 [1] where x, y, and z are non-negative integers. We can see that [1] is a congruence modulo 8: 3^y = z^2 (mod 8) [2] When z=1 and and y=2 we have 3^2 = 1 (mod 8) [3] and by Fermat's theorem. So this means that y must be...

wasn't too sure what you mean with the modulo 8, but this is what i have so far so z can't be even as its equal to an odd plus an even number = odd so when z=0, x=3 then z=3 and when y=2, x=4 then z=5 so if z^2-3^y has to be a perfect square then y has to be even and a power of 2 i.e...