Prime to square

Number Theory Level 3

Find all primes $p$ such that $17 p+ 1$ is a square number.

37 19 7 983

3 solutions

Jagadish Sai
Feb 18, 2019

X²=17p+1, x²-1=17p,( X+1)(x-1)=17p, Finally X+1 shows it's aprime 15,x-1=17 Hence p=19 proved

u hould not copy others solution

chakravarthy b - 10 months, 2 weeks ago

Nnsv Abhiram
Feb 18, 2019

a square minus 1 equals to 17 p then a equals to 18 , a plus 1 equals to p so 19

not copy,copy cat

Nnsv Abhiram - 2 years, 3 months ago

i posted the same solution on feb 10 and u posted on feb 18, seems obviousthat who is copy cat.

chakravarthy b - 10 months, 2 weeks ago

Chakravarthy B
Feb 10, 2019

If 17 p+1 = x^2, then 17 p=x^2 - 1 17p=(x+1)(x-1). Since x+1=17 implies that 15 is prime, x-1 = 17. Therefore, p = 19.

I think there is a typo in the problem, where you wrote 17p^2+1 instead of 17p+1.

Henry U - 2 years, 4 months ago

Now I changed the question

chakravarthy b - 2 years, 4 months ago

I am sure there is a typo in the problem, where you wrote 17p^2+1 instead of 17p+1.

A Former Brilliant Member - 2 years, 4 months ago

Now I changed the question

chakravarthy b - 2 years, 4 months ago