Answer
See below
Work Step by Step
a. To verify 3 | (25 - 19 ), we need to check whether the difference between 25 and 19 is divisible by 3.
25 − 19 = 6 and 3 | 6 since 6 = 3 * 2.
Therefore, 3 is indeed a divisor of ( 25−19 )
So, 3 | ( 25 − 19 ) is true.
b. 25 ≡ 19 ( mod 3 )
We have :
25 = 3 * 8 + 1 => gcd(25, 3) = 1
19 = 3 * 6 + 1 => gcd(19, 3) = 1
So, both 25 and 19 leave a remainder of 1 when divided by 3, therefore, we can say that 25 and 19 are congruent modulo 3:
25 ≡ 19 (mod 3)
c. 25 = 19 + 3k?
We have :
25 – 19 = 6 = 3 * 2
25 = 19 + 3 * 2
So value of k = 2 has the property that 25 = 19 + 3k.
