binomial

If 7^103 is divided by 25, then what is the remainder?

3 Answers

106
Asish Mahapatra ·

7^103 = 7*(50-1)51

So expanding binomially we get last term as -7 so remainder = -7 or 18

21
eragon24 _Retired ·

other way is using congruences

72≡ (-1)(mod25)
So
(72)51≡ (-1)(mod25)
7102≡ (-1)(mod25)
7103 ≡(-7)(mod25)
≡(18)(mod25)
So the remainder is 18

1
cute_cat ·

i had also got -7, the same way ashish got it...

but why did we add it to 25....???

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