Numerical answer
What is the remainder when 13¹⁵⁰ is divided by 7?
Show answer and solution
Answer: 1
13 ≡ 6 ≡ −1 (mod 7).
So 13¹⁵⁰ ≡ (−1)¹⁵⁰ = 1 (mod 7), since 150 is even.
Remainder = 1.
Tip: whenever the base is ≡ −1 (mod n), the parity of the exponent alone decides the remainder — no need for Fermat's theorem here.
So 13¹⁵⁰ ≡ (−1)¹⁵⁰ = 1 (mod 7), since 150 is even.
Remainder = 1.
Tip: whenever the base is ≡ −1 (mod n), the parity of the exponent alone decides the remainder — no need for Fermat's theorem here.
Saved on this device. Sign in or create a free account to keep it on every device.