Hello everyone,
I was wondering if anyone can help me with the explanation for question 241 in the OG11.
Question
If the integer n has exactly three positive divisors, including 1 and n how many positive divisors does n^2 have?
I read the explanation at the back but I don't understand if anyone can explain that would be great thanks!
OG 11 math problem solving question
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i did it by picking numbers and there are only 2 numbers 4 (three divisors 1 2 4) & 9 (1 3 9). and their squares 16 (1,2,4,8,16) and 81 (1,3,9,27,81)
so 5 is the answer.
there may be someother method but i did it this way. i hope it helps.
so 5 is the answer.
there may be someother method but i did it this way. i hope it helps.
lets consider the number to be 'n'. since it has only one more divisor other than 1 and n, n must be a perfect sqare. so say n=x^2(x is a prime).
=> n^2 = x^4
Now divisors of x^4 are 1, x, x^2, x^3, x^4.
i.e 5 divisors.
=> n^2 = x^4
Now divisors of x^4 are 1, x, x^2, x^3, x^4.
i.e 5 divisors.
-Wish u all the best,
Soumyajit.
Soumyajit.