Solve $x\equiv 1(mod5), x\equiv 2(mod6), x\equiv 3(mod7)$

modular-arithmetic number-theory chinese-remainder-theorem

Solution 1:

x % 5 = 1 = -4

x % 6 = 2 = -4

x % 7 = 3 = -4

This means x % LCM(5, 6, 7) = -4 x % 210 = -4

Therefore x = 210t - 4 (-4, 206, ...)

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