Question

How many positive integers n are there such that 450 divided by n leaves a remainder of 30?​

Answer 1

I'm assuming the question is meant to read:

10n≤n10

Python tells us:

>>> [n for n in range(1,100) if 10**n <= n**10]

[2, 3, 4, 5, 6, 7, 8, 9,10]

>>> len([n for n in range(1,100) if 10**n <= n**10])

9

But to actually think it out without Python-bashing:

1 doesn't grow from exponents, so 110 won't be bigger than 101 . We start at n=2 .

On the positive integers, both sides are strictly increasing, and we know the left side of the equation grows strictly faster than the right side, so once the left side is greater, it will remain greater.

At n=10 , we get 1010≤1010 .

Answer 2

Step-by-step explanation:

fourty to thirty position of integersvcan be pisitive