1. ## Contest problem 6

Find all positive numbers N with the following property: The greatest factor of N (other than N) is 6 times the smallest divisor of N (other than 1).

2. ## Re: Contest problem 6

Why are these being answered...I thought it was forbidden to post "contest" problems here.

Not only that, but Kanwar shows no work....

3. ## Re: Contest problem 6

these are practice problems sir

4. ## Re: Contest problem 6

Well, anybody can say that...I didn't make the existing rule...I'm just a helper...
Perhaps better NOT to use the word "contest"....

5. ## Re: Contest problem 6

Originally Posted by Kanwar245
Find all positive numbers N with the following property: The greatest factor of N (other than N) is 6 times the smallest divisor of N (other than 1).
Up to 10000 the only number with such property is 24 .

Small Maple program :

Code:
for N from 1 to 10000 do
for i from 2 to N do
if N mod i = 0 then
a:=i:
break;
end if;
end do;
for j from N-1 to 2 by -1 do
if N mod j = 0 then
b:=j:
break;
end if;
end do;
if b=6*a then
print(N);
end if;
end do;

6. ## Re: Contest problem 6

Originally Posted by Kanwar245
Find all positive numbers N with the following property:
The greatest factor of N (other than N) is 6 times the smallest divisor of N (other than 1).
Well, since no moderator has jumped in with the eviction papers, looks like that
rule has now been abolished....so:

u = greatest factor, v = lowest factor

If N is even, then no choice: v = 2 and u = N/2
So N/2 = 6v
N/2 = 12
N = 24

If N is odd, then u and v will be odd
But 6*(odd number) = even
So none if N is odd.

Heretoforth, henceforth and allforths, only N=24 is solution.