Question

What is the remainder when 2^70 + 3^70 is divided by 13?

Answer 1

Answer: hope it helps

Explanation:

2^6=64≡ -1 ( mod 13)

So 2^70=16*(2^6)^11=16*(-)^11(mod 13)

2^70 ≡-16 ( mod 13)

2^70 ≡10 ( mod 13)

Now 3^3=27≡1 ( mod 13)

So 3^70= 3*(3^3)^23≡ 3*(1)^23 ( mod 13)

≡ 3 ( mod 13)

Thus 2^70+3^70 ≡ 10+3 (mod 13)

≡ 0 ( mod 13)