EASY
IOQM - PRMO and RMO
IMPORTANT
Earn 100
Find the largest -digit number which is divisible by such that all integral power of end with
50% studentsanswered this correctly
Important Questions on Number Theory
HARD
IOQM - PRMO and RMO
IMPORTANT
The prime numbers and are such that Determine the sum of all possible values of
HARD
IOQM - PRMO and RMO
IMPORTANT
A five-digit number is such that when divided respectively by the remainders are What is the remainder when is divided by
HARD
IOQM - PRMO and RMO
IMPORTANT
Let be three distinct positive integers such that the sum of any two of them is a perfect square and having minimal sum Find this sum.
HARD
IOQM - PRMO and RMO
IMPORTANT
For a natural number , let denote the number obtained by deleting zero digits, if any. (For example, if if ). Find the number of -digit numbers for which is a divisor of different from
MEDIUM
IOQM - PRMO and RMO
IMPORTANT
Let the rational number , be closest to but not equal to among all rational numbers with denominator What is the value of
EASY
IOQM - PRMO and RMO
IMPORTANT
Find the smallest positive integer such that is a prime and is a perfect square.
HARD
IOQM - PRMO and RMO
IMPORTANT
How many ordered pairs of positive integers with and satisfy
HARD
IOQM - PRMO and RMO
IMPORTANT
Consider the set of all natural numbers such that when divided by respectively, the remainders, in that order, are distinct prime numbers in an arithmetic progression. If is the minimum number in find the sum of digits of .
Note: In PRMO-2019, original question was asking about maximum number in , which couldn't be calculated. So, this was the bonus question. Only minimum value can be calculated.
