Question

Determine all positive number replacements​ (less than the​ modulus) for the question mark that make the statement true. 6+​? =​(mod 7)

A.The positive number​ replacement(s) (less than the​ modulus) for the question mark​ is(are)

enter your response here.(Use a comma to separate answers as​ needed.)
B.There are no positive number replacements​ (less than the​ modulus) for the question mark that make the statement true.

Answer 1

To determine the positive number replacements (less than the modulus) for the question mark in the equation 6 + ? ≡ (mod 7), the positive number replacements are 1 + 7n, where n is a non-negative integer.

Step-by-step explanation:

To determine the positive number replacements (less than the modulus) for the question mark in the equation 6 + ? ≡ (mod 7), we need to find the numbers that, when added to 6, give a remainder of 0 when divided by 7. The modulus of 7 means that the remainders can only be integers from 0 to 6. By trying different numbers less than the modulus, we find that the positive number replacements for the question mark are 1, 8, 15, 22, 29, and so on. In other words, the positive number replacements are 1 + 7n, where n is a non-negative integer.