Question

7 4K ≡ ________________ (mod 100 )
(a ) 4
(b ) 2
(c) 3
( d ) 1​

Answer 1

I assume you're asked to find
`7^(4k)\pmod{100}` for positive integer k. To start, notice that

`7^4 \equiv 7^3*7 \equiv 343*7 \equiv 43*7 \equiv 301 \equiv 1\pmod{100}`

Then for every k, we have

`7^(4k) \equiv (7^4)^k \equiv 1^k \equiv 1 \pmod{100}`

Answer 2

Not sure 74k is 74000 so mod 100 gives to digits from the right. So answer is 0.
Or it’s 7^4 = 2,401 so answer is 1.
Please check the question again