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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

Quantity A

x-y

Quantity B

8


x and y are prime numbers

x+y is odd

x < y

Quantity A

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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