Question

Suppose that a and b are integers, a ≡ 4 (mod 13), and b ≡ 9 (mod 13). find the integer c with 0 ≤ c ≤ 12 such that

a.c ≡ 9a (mod 13).
b.c ≡ 11b (mod 13).
c.c ≡ a + b (mod 13).
d.c ≡ 2a + 3b (mod 13).
e.c ≡ a2 + b2 (mod 13). f ) c ≡ a3 − b3 (mod 13)

Answer 1

The student is asked to solve for an integer c that satisfies several conditions based on congruences of two given integers a and b modulo 13. While the provided solution texts are not applicable, such a problem typically involves using modular arithmetic rules to find an integer that meets all the specified relations.

Step-by-step explanation:

The student's question involves finding an integer c that satisfies several modular arithmetic conditions given two integers a and b with known congruences modulo 13. Since concrete values for a and b are not given in the question but their congruences are, we can use those congruence relationships to find a value for c that works for all of the given conditions. The problem essentially becomes a set of simultaneous modular equations that we must solve to find a correct value of c within the specified range.

However, without the correct congruences for a and b, the provided solution texts do not directly apply to this problem. It is important to assess the congruences for a and b correctly and use them to establish the value of c by meeting all given conditions.

Answer 2

the answer is B hope this helped