# Congruence problem

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Thread starter 1 month ago
#1
Solve the congruence problem x^15 ≡ 48 (mod 59).

x^15 ≡ 48 (mod 59) => x^3= ≡ 48^2 ≡ 3 (mod 59) ; why is this? How can we show that 48^2 ≡ 3 (mod 59)?
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1 month ago
#2
(Original post by username42530853)
Solve the congruence problem x^15 ≡ 48 (mod 59).

x^15 ≡ 48 (mod 59) => x^3= ≡ 48^2 ≡ 3 (mod 59) ; why is this? How can we show that 48^2 ≡ 3 (mod 59)?
One simple way is to note that

So

48^2 mod 59 is the same as 11^2 mod 59

and this is much easier to work out as 3 mod 59.
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