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A Quintic Problem (Posted on 2006-03-15) Difficulty: 3 of 5
Determine all possible integer solutions, whether positive or negative, to this equation:

5y4 + 2560y2 = x5 - 65536

See The Solution Submitted by K Sengupta    
Rating: 2.3333 (3 votes)

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re: Small steps (another step) Comment 7 of 7 |
(In reply to Small steps by Gamer)

5*(y2 + 256)2 = x5 + 2^18

implies x^5 + 2^18 is a multiple of 5.

2^18 is congruent to 4 mod 5, so x^5 is congruent to 1 mod 5.

This implies x is congruent to 1 mod 5.

The known solution x=16 fits this, but I'm stuck.


  Posted by Jer on 2006-03-16 12:53:05
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