Question

6.29 Theorem. Ifa is an integer and v and n ane natural mumbers such that (a,n) 1, then a)+1a (mod n) Now let's apply these observations to solve actual congrucnces 6.30 Question. Consider the congruence x2 (mod 7). Can you think of an appropriate operation we can apply to bath sides of the congruence that would allow us to "solve" for x? If so, is the walue obiained for x a solution to the original congruence? 6.31 Question. Consider the congruence x37 (mod 10). Can you think of an appropriate operation we can apply to both sides of the congruence that wuld allow us to "solve" for x? If so, is the value obtained for x a solution to the original congruence?

Answer 1

9.6.30 ged tr, bln)e Sx (-1)-6x1- 1 V2 1 22 mod1) iucd 7) 7 mod 1 tp.31 pin 16 2 4 3Y 1t1 YxI-3Y 1 2 e- mod 16 2 3 mod lo