Question

Carry out the following calcula- tions by hand by using the Chinese Remainder Theorem to split each operation into two operations modulo smaller numbers. You must show your work to receive full credit. (a) 23 x 36 mod 55 (b) 29 x 51 mod 91

Answer 1

Explanation:

We have
`55 = 5 x 11`

23 x 36 mod 5 = 3 (since unit digit is 8)

23x36 mod 11 =3

Since 5 and 11 are prime we get

23x36 mod 55 = 3 mod 55

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b) 91 = 13 x7

`29x51 mod 7 = 2\\29x51 mod 13 = 10\\`

29x51 mod 91 =23