Difference between revisions of "2023 IOQM/Problem 9"
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==Problem== | ==Problem== | ||
| − | Find the number of triples <math>(a, b, c)</math> of positive integers such that | + | Find the number of triples <math>(a, b, c)</math> of [[positive integers]] such that |
| − | (a) <math>ab</math> is a prime; | + | (a) <math>ab</math> is a [[prime]]; |
| − | (b) <math>bc</math> is a product of two primes; | + | |
| − | (c) <math>abc</math> is not divisible by square of any prime and | + | (b) <math>bc</math> is a product of two [[primes]]; |
| − | (d) <math>abc | + | |
| + | (c) <math>abc</math> is not divisible by [[square]] of any [[prime]] and | ||
| + | |||
| + | (d) <math>abc\leq30</math> | ||
Revision as of 07:06, 20 October 2023
Problem
Find the number of triples 
of positive integers such that
(a) 
is a prime;
(b) 
is a product of two primes;
(c) 
is not divisible by square of any prime and
(d) 
