( 5 n 4 + 3 ) (5n^4+3)

What is the least positive integer n n such that ( 5 n 4 + 3 ) (5n^4+3) is a prime number?


The answer is 2.

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1 solution

Munem Shahriar
Oct 28, 2017

Positive integers start from 1 , 2 , 3 , 4 , 5 , 1,2,3,4,5,\ldots

For n = 1 , n = 1,

5 n 4 + 3 5n^4 + 3

= 5 ( 1 ) 4 + 3 = 5(1)^4 +3

= 8 Not a prime number . \space \space ~~~~~~ ~~~~~~~~ ~~~~~ = 8 \longrightarrow \color{#D61F06}\text{Not a prime number}.

For n = 2 , n =2,

5 n 4 + 3 5n^4+3

= 5 ( 2 ) 4 + 3 = 5(2)^4 + 3

= 83 Prime number \space \space ~~~~~~ ~~~~~~~~ ~~~~~= 83 \longrightarrow \color{#20A900}\text{Prime number}

Hence n = 2 n = \boxed{2} is the least integer.

Is there any better way to do this ? Like what if i asked the largest integer less than 1000 satisfying this

Sabhrant Sachan - 3 years, 7 months ago

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