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Let a(31+51+71)1(mod11). What is the remainder when a is divided by 11?

 May 3, 2022
edited by hhhhh  May 3, 2022
 #1
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You can compute that a = 27, so the remainder is 5.

 May 3, 2022
 #2
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Thank you for attempting to help, but the answer is actually 10, as i just found.

hhhhh  May 3, 2022
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Note that 11×1+1=12=3×4, so 3 and 4 are multiplicative inverses of each other mod 11.

Similarly, we have 11×4+1=45=5×9 so 5 and 9 are multiplicative inverses of each other mod 11.

Also, 11×5+1=56=7×8 so 7 and 8 are multiplicative inverses of each other mod 11.

 

Therefore, a(31+51+71)1(4+9+8)1211(mod11)1110(mod11).

 May 3, 2022

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