Thread: 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).

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

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

these are practice problems sir

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"....

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;

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.