High School

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List all of the integers that are congruent to 1 modulo 22.

A. -43, 1, 23, -12, 45, 89
B. -43, 1, 23, 45
C. 1, 23, -12, 89
D. 23, 45, 89

Answer :

Final answer:

The integers between -43 and 89 that are congruent to 1 modulo 22 are -43, 1, 23, 45, and 89.

Explanation:

The student is asking to list all integers between -43 and 89 that are congruent to 1 modulo 22. Two numbers are congruent modulo a number when they have the same remainder upon division by that number. In this case, we're looking for numbers congruent to 1 modulo 22, meaning they leave a remainder of 1 when divided by 22. To solve this, we can either use a trial and error method for each number or calculate by adding or subtracting multiples of 22 to/from 1 to find the other numbers. After performing the calculations or checks, you will see that the integers between -43 and 89 that satisfy this condition are: -43, 1, 23, 45, 89. The number -12 does not fit this criterion as it is congruent to -12 modulo 22 (or, equivalently, 10 modulo 22), not 1 modulo 22.

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