practice problems pending

Q1. Solve for x:
32x = 79 mod 1225
S1.
32x = 79 mod 25 => 7x = 4 mod 25, since 7*3 = 21 = -4 m 25 => 7*-3 = 4 m 25 => x = 22 m 25
32x = 79 mod 49 => 32x = 30 m 49 => 16x = 15 m 49, since 16.4 = 64 = 15 m 49 => x = 4 m 49

Use CRT now:
x = p.25 + q.49
m 25
22 = q.-1 m 25 => q = -22 = 3 mod 25
m 49
4 = p.25 mod 49
=> p = 8 mod 49, since 25.8 = 200 = 4 mod 49
x = 8.25 + 3.49 mod 1225 = 347 mod 1225

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