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Find the least positive four-digit solution to the following system of congruences.

 

7x = 21 (mod 14)

2x + 18 = 16 (mod 9)

 May 6, 2021
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7x = 21 (mod 14)

x = 3 (mod 14)

2x = -2 (mod 9)

x = -1 (mod 9)

x = 8 (mod 9)

x = 3 (mod 14)

x = 17

x = 17 + 14*9*a, where a is an integer. 

Find the least positive four-digit solution. 

 

=^._.^=

 May 6, 2021

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