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

Quantity A

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

Quantity B

1


How many positive three-digit integers with an odd hundreds digit are multiples of 5?
When 2($$10^{100}$$)+1 is divided by 3, the remainder is r.

Quantity A

r

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 the 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


Condition 1: n is a positive integer that is less than100

Condition 2: When n is divided by 5, the remainder is 3

Condition 3: When n is divided by 6, the remainder is 2

Quantity A

The number of values of n that satisfy the three conditions

Quantity B

4


If n=$$k^{2}pr^{3}$$, where k, p, and r are different prime numbers, what is the least possible value of n?
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?
1575=$$3^{x}$$*$$5^{y}$$*$$7^{z}$$,What`s the value of x+y+z?

Quantity A

The number of different prime factors of 12

Quantity B

The number of different prime factors of 9


Quantity A

The number of prime factors of 27

Quantity B

The number of prime factors of 18


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