#### Quantity A

The remainder when ($123^{4}$-$123^{3}$+$123^{2}$-123) is divided by 122

#### Quantity B

2

X=$233^{4}$-$233^{3}$+$233^{2}$-233

What is the remainder when X is divided by 232?
X=$123^{4}$-$123^{3}$-$123^{2}$-123

What is the remainder when X is divided by 122?
What is the remainder of $\frac{132^{5} - 2(132^{4}) + 6(132^{3} )- 3(132)}{65}$ ?

#### Quantity A

The remainder when the difference of $3191^{2020}$ and $3159^{2020}$ is divided by 16

#### Quantity B

1

How many three-digit positive numbers are divisible by 5 and have a hundreds digit which is an odd number?

#### Quantity A

The remainder when 2*$10^{1000}$+1 is divided by 3

#### Quantity B

1

If p is an prime number greater than 5,and if 5 is a factor of p+$p^{2}$,which of the following might be the remainder when p is divided by 5?

Indicate all such numbers.
How many integers between 100 and 1000 have a tens digit equal to 9 and are multiples of 4?
When positive integer n is divided by 4, the remainder is 3; when n is divided by 3, the remainder is 2.

#### Quantity A

The least possible value of n

#### Quantity B

12

n satisfies the following three restraints at the same time.

a) n is a positive integer less than 100

b) the remainder is 2 when n is divided by 6

c) the remainder is 3 when n is divided by 5

#### Quantity A

The total number of all the possible values of n

#### Quantity B

4

y=$a^{2}$*b*$c^{3}$, and a, b, c are different prime numbers. What is the minimum value of y?
x > y

x and y are prime numbers and x+y=16

x-y

#### Quantity B

8

x and y are prime numbers

x+y is odd

x < y

x

#### Quantity B

3

The integer k is the product of four different prime numbers. If the result when k is divided by 10 is a multiple of 11, which of the following could be the result when k divided by 5?
Among all the prime numbers within 15

#### Quantity A

The product of them all

#### Quantity B

The greatest prime number to the power of 5

The number of children in a certain family is a prime number less than 10. The number of boys in the family is greater than the number of girls, and the number of boys is a prime number. If at least 1 of the children in the family is a girl, which of the following could be the number of boys in the family?

Indicate all such numbers.
Two different prime numbers are greater than 2 and less than 50. If the product of them is less than 100, then how many combinations of them will there be?
0 < P*Q < 100, P and Q are both prime numbers,and P < Q, how many combinations of P and Q are there?
How many positive integers no greater than 20 can be expressed as the sum of two different prime numbers?
1 2 ... 4 5 6 7 8 9 10 ... 24 25

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