perplexus.info :: Just Math : Divisibility

Divisibility (Posted on 2004-01-06)

For how many natural numbers x, is the expression: (x ² + 2x + 3) divisible by 35 ?

See The Solution Submitted by Ravi Raja

Rating: 2.5000 (6 votes)

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Simplest solution - no moduli!

| Comment 10 of 11 |

Consider f(x) = x^2 + 2x + 3 = 0

The discriminant, b^2 - 4ac < 0.

Hence, f(x) is prime for all real x , i.e., it is NOT evenly divisible by 35 (or any other real number.)

QED

Posted by JayDeeKay on 2016-06-10 10:23:34

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