In June, Casey counted the months until he would turn 16, the minimum age at which he could obtain his driver’s license. If the number of months Casey counted until his birthday was 45, in what month would Casey turn 16? 

Find the minimum value of \(36^m-5^n\) with \(m,n\in Z\)+

Find the maximum value of \(\dfrac{x}{x+y}+\dfrac{x}{8-\left(x+y\right)}\) with \(x,y\in N\)

Find the minimum value of \(E=2x^2+2xy+5y^2-8x-22y\)

Find the maximum value of \(\dfrac{x^2}{x^4+1}\)

Given xy = 1.  Find the minimum value of \(\left|x+y\right|\)

Find the minimum value of \(A=\left|x-3\right|+\left|x-7\right|\)

What is the sum of the integers strictly between 1 and 100 that are multiples of neither 2 nor 5?

Jennie Weiner has p pennies, n nickels, d dimes and q quarters with a total value of $1.08. If the numbers p, n, d and q are distinct and positive, and the greatest common divisor of each pair of these numbers is 1, what is the least possible value of p + n + d + q?

The graph of the line 3x − 4y = 13 is translated 2018 units to the right. What is the y-intercept of the translated line? Express your answer as a decimal to the nearest hundredth.

Three days ago, there were p cupcakes on the counter. Two days ago, exactly 20% of the cupcakes were eaten. Today, there are 30% fewer cupcakes than yesterday and half as many as there were three days ago. If a whole number of cupcakes were eaten every day, what is the least possible value of p?

What is the area of a 60 degree sector of a circle with radius 30 feet? Express your answer in terms of π.

Find \(n\in Z\) such that: \(n^3-n^2+2n+7⋮n^2+1\)

Prove that with \(n\in Z\)

\(n^2-5n-49⋮169̸\)

Prove that with \(n\in Z\)

\(n^2+7n+22⋮̸9\)

Prove that with all \(a,b,c,d\in Z\)

\(\left(a-b\right)\left(a-c\right)\left(a-d\right)\left(b-c\right)\left(b-d\right)\left(c-d\right)⋮12\)

Find n so that: \(3^n-1⋮8\)

Find n so that \(5^n-2^n⋮63\)

Find the last 3 digits of \(3^{100}\)

Find n so that: \(1^n+2^n+3^n+4^n⋮5\)