0
votes
3answers
91 views

Finding K value to solve a problem using diophantine equation

I have to prove that any number that divided by 5 gives a remainder of 1 and divided by 7 a remainder of 2, also gives a remainder of 16 when divided by 35, using a diophantine equation. So first I ...
1
vote
0answers
309 views

Is this Diophantine equation proof correct?

It's probably a good thing I decided to try working on problems from the book. This section seems to be proving difficult. In any case, I'm asked to prove that $x^4+4y^4=z^2$ has no non-trivial ...
5
votes
4answers
183 views

Use induction to prove a product of sums of squares is a sum of squares

For any natural number $n\ge 1$, given pairs $(a_1,b_1),(a_2,b_2),...,(a_n,b_n)$ of integer numbers, there exist integer number $c$ and $d$ such that $$\prod_{i=1}^{n}(a_i^2+b_i^2) = c^2+d^2$$ My ...