# Numbers

Find the prime number p such that 71p + 1 is a perfect square.

### See our previous ‘Questions of the Day’:

1. 71p+1=n^2
then (n-1)(n+1)=71
only possibility aren-1=71 or n+1=71 . therefore p=73

2. Abhishek Tandon

I never thought this would happen the solution came in my dream.

P=73

71p+1
71 is also a prime no. So if p=71 then it will be p^2 +1 this is not a perfect square

If (p+2)*p+1 =p^2+2p+1=(p+1)^2
Next prime is 73
73=71+2

73*71+1= 72^2=5184

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