One for practice

Find all positive solutions to the following Diophantine equation ------

a 4 + b 4 + c 4 + d 4 + e 4 + f 4 + g 4 + h 4 = 26959 .

2 Answers

341
Hari Shankar ·

Hint: modulo 5

3
minch ·

equation can be written as:
(a4-1) + (b4-1)+(c4-1) + (d4-1)+(e4-1) + (f4-1)+(g4-1) + (h4-1)=26951
L.H.S is a multiple of 5 but R.H.S is not, hence no solution.

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