Find the unit digits of the large powers problems.

A positive integer is subtracted from its square. Which of the following could be the units digit of the final result?

n^2 -1 is divisible by 8 if n is

The product of three consecutive integers is divisible by

The product of two consecutive integers is divisible by

When the positive integer m is divided by 7, the remainder is 4. What is the remainder when 2m is divided by 7 ?

If a and b are numbers such that (a − 4)(b + 6) = 0, then what is the smallest possible value of a^2 + b^2 ?

A particular integer N is divisible by two different prime numbers p and q. Which of the following must be true?

I. N is not a prime number.

II. N is divisible by pq.

III. N is an odd integer.

If p is a prime number, how many factors does p^3 have

If n is positive integer, show that n(n^2-1)(n^2-5n+26) is divisible by 120

If n is positive integer (n>0), show that n^4-3n^2+9 is composite number

If n is positive integer, find the value of n such that n^4-16n^2+100 is a prime number

Find the remainder of \dfrac{5^{22}+7}{8}

Express the following squares as the sum of two consecutive integers.

If a,b are natural numbers such that 2a+ab+\dfrac{a}{b} =243

find the values of a,b