UPSC CDS I 2025 Mathematics Paper

Expression: 2p−1
Divisor: p
Calculations:
We need to find the remainder when 2p−1 is divided by p .
Since p is a prime number greater than 5 : Direct putting value p=7.
Substitute p=7 into the expression:
Expression =27−1
27=128
Expression = 128−1
⇒ Expression = 127
Now, we need to divide 127 by p=7 and find the remainder.
127÷7
127=7×18+1
The remainder when 27−1 is divided by 7 is 1.