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 by Daniel)
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
This gives
y(x!-1)/x>x
y(x!-1)>x^2
y>x^2/(x!-1)
now for b>y
y(x!-1)/x>y
y(x!-1)>yx
y(x!-1-x)>0
so y>0 and x!-1-x>0
x!>x+1
this is true for all x>2
So to summarize, it would seem that as long as we have both
x>2
and
y>x^2/(x!-1)
Then we will get a valid base with b=y(x!-1)/x
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Posted by Daniel
on 2018-06-01 11:35:36 |
re: beyond base 10, analytical solution
