binomial

7^103 = 7*(50-1)⁵¹

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

other way is using congruences

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

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

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