Answer
Check Explanation
Step-by-step explanation
a ≡ b (mod n)
This means a and b have the same remainder when they are divided by n
So, to check if this question works out, we divide what is on the left hand side and what is on the right hand side by what is after the mod.
1) 67 × 73 ≡ 1 × 3 (mod 5)
4891 ≡ 3 (mod 5)
So, to check,
(4891/5) = 978 remainder 1
(3/5) = 0 remainder 3
The remainders are different.
So, this equation is wrong and does not work.
This equation is false.
2) 83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)
Noting that it is the units digit that determines the remainder
3 raised to the power of a multiple of 4 gives 81 raised to the power of a positive integer
5 raised to power of a multiple of 4 gives 625 raised to the power of a positive integer
So, using these numbers,
83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)
81 ≡ 625 (mod 17)
(81/17) = 4 remainder 13
(625/17) = 36 remainder 13
The remainders are the same.
So, this equation is correct and it works.
This equation is true.
Hope this Helps!!!