(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] larsen problem

1. The problem statement, all variables and given/known data

Determine all integral solutions of [itex]a^2+b^2+c^2=a^2 b^2[/tex]. (Hint: Analyze modulo 4.)

2. Relevant equations

3. The attempt at a solution

a^2,b^2,c^2 are congruent to 0 or 1 mod 4 implies that a^2,b^2,c^2 are all congruent to 0 mod 4. This implies that a,b,c are even.

[tex]a=2a_1, b=2b_1, c=2c_1[/tex]

Then we have [itex]a_1^2+b_1^2+c_1^2 = 4a_1^2 b_1^2[/itex]. Now it is very clear that a_1^2,b_1^2,c_1^2 are all congruent to 0 mod 4.

Let [itex]a_1=2a_2,b_1=2b_2,c_1=2c_2[/itex].

If we keep doing this, we get 3 decreasing sequences of positive integers that never reach zero, which is impossible.

Therefore there are no solutions.

Is that right?

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# Homework Help: Larsen problem

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