Is there a way to differentiate between numbers

In summary, if we do not know the factors of a number, and we do not want to factor them, then the numbers will have the same last two digits.
  • #1
epsi00
84
0
like N=5053=163*31 and N=169*37=6253 if we do not know the factors and if we do not want to factor them. They both have the same last two digits.
I can't think of any test to apply to this kind of numbers ( it's in fact a family of numbers that share the same last two digits but are product of (last digit only ) 3*1 or 7*9 ).
 
Physics news on Phys.org
  • #2
Here's what I understand from your post. You have two disjoint sets of numbers, A and B. You want a method to determine whether a number is a member of set A or set B under the assumption that it is in one of those, without factoring the number.

If that's right, would you define A and B more precisely?
 
  • #3
CRGreathouse said:
Here's what I understand from your post. You have two disjoint sets of numbers, A and B. You want a method to determine whether a number is a member of set A or set B under the assumption that it is in one of those, without factoring the number.

If that's right, would you define A and B more precisely?

That's correct. A and B both are of the form 6*k+1. and multiplication ( within each set ) of two numbers ( whose last digits can be a 3*1 or a 7*9) (from the two different sets) always produces two numbers with the last two digits ( not necessarily 53 and not necessarily the same) 13 or 33 or 93 or 73).

example:
163*31 = 5053 a number produced by a 3*1 multiplication ( last digits only )
169*37 = 6253 a number produced by a 9*7 multiplication ( last digits only )

another example would be:
133*61 = 8113
139*67 = 9313

but also
103*31 = 3193
109*37 = 4033

I am interested in finding out a test by which, given a number, we can say it's a "3*1" product or a 7*9 ( without having to factor the number ).

thanks
 
  • #4
What if you can't? 2673 = 81*33 = 27*99
 
  • #5
hamster143 said:
What if you can't? 2673 = 81*33 = 27*99


your number is not a product of a 6k+1 by another 6k+1. Those numbers obey different rules.
I am only interested in numbers of the form 6*k+1.

multiplication of numbers of the form (6j+1)(6i+1) have periodic "last two digits" like I wrote in my earlier post. So just looking at the last two digits of a number will not tell us if that number was a product of a 3*1 or a 7*9 because these two products produce the same last two digits ( 13, 99, 73 and 53 ). Here 3*1 and 7*9 refer only to the last digit of the factors making up a number. ( 163*31 is a 3*1 product ).
 
  • #6
epsi00 said:
your number is not a product of a 6k+1 by another 6k+1. Those numbers obey different rules.
I am only interested in numbers of the form 6*k+1.

Okay then, 31*343 =(6*5+1)*(6*57+1) = 49*217 = (6*8+1)*(6*36+1) = 10633.
 
  • #7
hamster143 said:
Okay then, 31*343 =(6*5+1)*(6*57+1) = 49*217 = (6*8+1)*(6*36+1) = 10633.

true again but so what? I am talking about the general case where the 3*1 number is not of the same value as a 7*9. I consider pairs of numbers, one of each kind.
to 31*343 can be associated 37*349 and I don't think these two are the same.
to 49*217 can be associated 43*211 and I again don't think that they have the same value.

the original question was about a test to tell the difference between a 3*1 and 7*9 number without having to factor them. In some cases the value is the same and my question loses its meaning but like I said I am talking about pairs such that:

N = p*q = a 3*1 number
M = (p+6)*(q+6) = a 7*9 number.

and all the examples I gave are of pairs ( in one of my previous posts )

so is there a test to tell the difference between the two.
 

1. Can numbers be differentiated based on their value?

Yes, numbers can be differentiated based on their value. This is the most common way of differentiating between numbers. For example, the number 5 is different from the number 10 because they have different values.

2. Is there a way to differentiate between positive and negative numbers?

Yes, positive and negative numbers can be differentiated by their sign. Positive numbers have a "+" sign in front of them, while negative numbers have a "-" sign. For example, 5 is positive while -5 is negative.

3. How can we differentiate between whole numbers and decimals?

Whole numbers and decimals can be differentiated by their decimal point. Whole numbers do not have a decimal point, while decimals do. For example, 5 is a whole number while 5.5 is a decimal.

4. Is there a way to differentiate between rational and irrational numbers?

Yes, rational and irrational numbers can be differentiated by their ability to be written as a fraction. Rational numbers can be expressed as a ratio of two integers, while irrational numbers cannot. For example, 1/2 is a rational number while √2 is an irrational number.

5. How can we differentiate between real and imaginary numbers?

Real and imaginary numbers can be differentiated by their imaginary component. Real numbers do not have an imaginary component and can be plotted on a number line, while imaginary numbers have an imaginary component and cannot be plotted on a number line. For example, 5 is a real number while √-1 is an imaginary number.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
9
Views
1K
  • Programming and Computer Science
Replies
1
Views
888
  • Calculus and Beyond Homework Help
Replies
32
Views
2K
  • Programming and Computer Science
Replies
1
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
32
Views
3K
  • Beyond the Standard Models
Replies
7
Views
606
  • Linear and Abstract Algebra
Replies
15
Views
4K
  • Thermodynamics
Replies
5
Views
814
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
4
Views
6K
Back
Top