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How to solve the following linear congruence equations?
Solution: 1)∫(22 1, 5 1) =17 ((22 1, 5 1) means 221and 5/.

And 17│85 (17│85 means that 17 is divisible by 85, the same below).

∴ congruence formula 5 1x≡85(mod22 1) has a solution.

∫5 1x≡85(mod 22 1)= & gt; 17 * 3x≡ 17 * 5(mod 13 * 17)

= = & gt3x≡5(mod 13)

= = & gt4*3x≡4*5(mod 13)

= = & gt( 13- 1)x≡2 * 13-6(mod 13)

= = & gt-x≦-6(mod 13)

= = & gtx≡6(mod 13)

All solutions of congruence formula 5 1x≡85(mod22 1) are

x≡6, 19,32,45,58,7 1,84,97, 10, 123, 136, 149, 162, 175, 188,20 1

2) ∫ (143,77) =11,and 1 1│572.

∴ congruence formula 143x≡572(mod77) has a solution.

∫ 143 x≡572(mod 77)= = & gt; 1 1 * 13x≡ 1 1 * 52(mod 1 1 * 7)

= = & gt 13x≡52(mod7)

= = & gt(7*2- 1)x≡7*8-4(mod7)

= = & gt-x≦-4(mod7)

= = & gtx≡4(mod7)

All solutions of the congruence formula 143x≡572(mod77) are

x≡4, 1 1, 18,25,32,39,46,53,60,67,74 (mod77)。