A number theory problem by Mohd Aasif
Number Theory
Level
2
Find the remainder when divided by 10.
5
1
6
0
2
3
7
4
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23 ≡ 3 mod 10
23^5 ≡ 3^5 mod 10
3^5 = 9(27) = 270 - 27 = 243 = 240 + 3
Therefore,
23^5 ≡ 3 mod 10
Meaning that 23^5 divided by 10 will have remainder 3.
You could get the same answer using binomial (20+3)^5 , when expanded, every term will be divisible by 10 except the last one, namely 3^5 , which will have remainder 3 as shown above.