a.What two-digit number equals the product of units' digit by the factorial of tens' digit?
b. What if a non-decimal system (base below ten) were allowed?
(In reply to beyond base 10, analytical solution
ok, I thought I had checked to make sure that the b calculated would always be greater than x and y but I see I had made a mistake in my calculation. Below is a derivation of restrictions on x,y to allow for a viable base
we need b>x and b>y
I'll start with b>x
now for b>y
so y>0 and x!-1-x>0
this is true for all x>2
So to summarize, it would seem that as long as we have both
Then we will get a valid base with b=y(x!-1)/x
Posted by Daniel
on 2018-06-01 11:35:36