gist the sum and substance of an argument. 5a(1) : the result of adding numbers the sum of 5 and 7 is 12. (2) : the limit of the sum of the first n terms of an infinite series as n increases indefinitely. b : numbers to be added broadly : a problem in arithmetic.
Re: A sum!
Posted: Tue Jan 15, 2019 7:55 am
sum noun (TOTAL) [ S ] the whole number or amount when two or more numbers or amounts have been added together: The sum of 13 and 8 is 21.
First of all note that $10! = 2^8 \cdot 3^4 \cdot 5^2 \cdot 7$ hence
$10!$ is not a perfect square,
$10!$ has $(8+1)(4+1)(2+1)(1+1) = 270$ divisors.
If $d \mid 10!$ , then there exists $p$ such that $dp =10!$ meaning that $p$ is also a divisor of $10!$. We also note that if one of $p, q$ is less than $10!$ then the other is greater than $10!$. Note that the case $p=q$ is impossible since $10!$ is not a perfect square.
Taking into account the addent that corresponds to $d$ along with the addent that corresponds to $p$ , we get: