Let $d$ be a positive number such that when $109$ is divided by $d$, the remainder is $4.$ Compute the sum of all possible two-digit values

Question

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Let be a positive number such that when is divided by , the remainder is Compute the sum of all possible two-digit values of .

Guest Jan 22, 2023

Guest · Answer 1 · 2023-01-22T04:10:17

The possible values of d are 14, 28, and 66, so the answer is 14 + 28 + 66 = 108.

Guest · Answer 2 · 2023-01-22T06:16:41

a=10; c=109 % a; if(c==4, goto3, goto4);printa; a++;if(a<100, goto1, 0)

15, 21, 35

109 mod 15 ==4 - Remainder

109 mod 21 ==4 - Remainder

109 mod 35 ==4 - Remainder

Two-digit moduli ==15 + 21 + 35 ==71