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Zero is the last digit of S (Posted on 2018-06-16)

Let S = a^5 + b^5 + c^5 + d^5, and
a,b,c,d are integers fulfilling a+b+c+d=0
Prove that S must be divisible by 10.

No Solution Yet Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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re: Answer

| Comment 2 of 3 |

(In reply to Answer by Math Man)

Nice solution.

We can easily extend this to a more general result:

Given any get of integers that sum to zero, the sum of the fifth powers of these integers is divisible by 10.

(Or, indeed, we can extend to any modulus and any other power that is a multiple of 5)

Posted by Jer on 2018-06-17 17:10:27

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