Question 120
A natural number $x$ is good if $x$ is the product of an even number (not necessarily different) primes. Be $a, b$ natural numbers and define $m(x) = (x+a)(x+b)$.
a. Prove that natural numbers $a, b$ exist, so $m(1), m(2), \ldots, m(2010)$ are all good numbers.
b. is $m(x)$ for every natural number $x$ good, then $a = b$ applies.
a. Prove that natural numbers $a, b$ exist, so $m(1), m(2), \ldots, m(2010)$ are all good numbers.
b. is $m(x)$ for every natural number $x$ good, then $a = b$ applies.