Modulus in Congruence

Question

I was proving a function to be onto but got stuck at point

(7 mod 15) * (? mod 15) = 1 mod 15 I need some value at ? .So that I can get 1 mod 15.

Thank you very much . Every help is appreciated

What is your function? How about ?=13? $7\cdot 13=91=6\cdot 15+1$ — Cornman, Nov 17 '17 at 02:30
You could use the extended Euclidean algorithm to solve $7 x + 15 y = 1$, but a brute-force search won't take very long. — Robert Israel, Nov 17 '17 at 02:33
@Cornman Yes it really solved my problem , Thank you very much. I totally skipped this. — Randhawa, Nov 17 '17 at 02:33

score 2 · Accepted Answer · answered Nov 17 '17 at 02:34

In order for the modular inverse of $7\bmod 15$ to exist at all, you need $\gcd(7,15)=1$, which is true here.

Since $\color{red}{2}\cdot 7\equiv 14\equiv \color{red}{-1} \bmod 15$, you will have $\color{red}{-2}\cdot 7\equiv 1 \bmod 15$. And $-2\equiv 13\bmod 15$.

Modulus in Congruence

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