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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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Answer
| Comment 1 of 3
For any number x, x^5=x mod 10. We can see this from the 5th powers of 0 to 9.
0^5=0
1^5=1
2^5=32
3^5=243
4^5=1024
5^5=3125
6^5=7776
7^5=16807
8^5=32768
9^5=59049
Then, S=a^5+b^5+c^5+d^5=a+b+c+d mod 10. Therefore, S=0 mod 10, so S is divisible by 10.
Posted by
Math Man
on 2018-06-16 19:53:51
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