I'm not sure how to start. Is 2310 some special number?
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6Yes, it's a special number: 2310 =235711 – Bram28 Mar 05 '17 at 00:14
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@J.G.: How would that work? The sum of two positive multiples of $2310$ can't be $2310$. – hmakholm left over Monica Mar 05 '17 at 00:27
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Also $2310$ is a square-free number,I guess that makes it special. – kingW3 Mar 05 '17 at 00:37
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@Henning I think J.G. meant two divisors of that number, e.g., 1155 + 1155. Although... their product, 1334025, is clearly odd. – Robert Soupe Mar 05 '17 at 02:16
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$$a + b = N$$
Let $N\mid a\cdot b$. If $p$ is some prime such that $p\mid N$, then both $a$ and $b$ are definitely divisible by $p$.
$2310$ is made up of $5$ different primes. So, if $N\mid a, b$, then both $a$ and $b$ are divisible by $N$. So, $N = a + b \ge 2N$. Contradition.
kingW3
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Andrei Kulunchakov
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@GerardL., it means that $a\cdot b = Nm$ for some integer $m$ – Andrei Kulunchakov Mar 05 '17 at 11:19
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If $a+b=2310=235711$, then both $a,b$ are odd, even. Let, $a=2308=22577, b=2; a=2307=3769, b=3$. Get that both $577, 769$ are primes, although not concerned with the problem as if change $2310$ to $2312=21156=22578=222289$, still the same issue persists. To prove, their product $2310 \not | ,,, ab$, need show there is different set of primes in each. Might be need a different approach as at:https://math.stackexchange.com/q/714294/424260 – jiten Nov 28 '20 at 19:51