Browse · MATH Print → jmc number theory senior Problem Given that 13−1≡29(mod47), find 34−1(mod47), as a residue modulo 47. (Give a number between 0 and 46, inclusive.) Solution — click to reveal Note that 34≡−13(mod47). Hence, 34−1≡(−13)−1≡(−1)−1⋅13−1≡(−1)⋅29≡18(mod47). Final answer 18 ← Previous problem Next problem →