IPMAT Indore Number System > HCF & LCM PYQs

The number of integers $n$ such that $1 \leq n \leq 10^7$ and $\gcd(n, 10^7) = 10^3$ is ___

When the square of the difference of two natural numbers is subtracted from the square of the sum of the same two numbers and the result is divided by four, we get

In a division problem, the product of the quotient and the remainder is 24 while their sum is 10. If the divisor is 5 then the dividend is __________.