# What Do You Know About Proizvolov's Identity?

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When it comes to mathematical expressions or equations, Proizvolov's identity is described as the identity that deals with the summation of the difference of the integers that are positive. The identity was discovered by Vyacheslav Proizvolov and has been used to solve numerous mathematical problems. We will like to test your knowledge about this theorem in this short quiz.

• 1.

• A.

1976

• B.

1985

• C.

1987

• D.

1990

B. 1985
• 2.

### Where was the theorem discovered?

• A.

• B.

1985 Olympic Games

• C.

Great Britain Theater

• D.

Soviet Union Square

Explanation
The theorem was discovered during the Soviet Student Olympiads.

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• 3.

### For Proizvolov's identity, what is S equal to?

• A.

N^2

• B.

N^3

• C.

2n

• D.

N-2

A. N^2
Explanation
Proizvolov's identity states that S is equal to n^2. This means that the value of S is obtained by squaring the value of n.

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• 4.

### When n=2, what is S equal to?

• A.

8

• B.

0

• C.

4

• D.

6

C. 4
Explanation
When n=2, the value of S can be determined by substituting n=2 into the equation or expression given in the question. However, since the equation or expression is not provided, it is not possible to determine the value of S. Therefore, an explanation for the correct answer is not available.

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• 5.

### When n=3, what is S equal to?

• A.

6

• B.

27

• C.

9

• D.

1

C. 9
Explanation
When n=3, the value of S can be calculated by substituting 3 into the equation. S = n^2, so S = 3^2 = 9.

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• 6.

### When n = 4, what is S equal to?

• A.

16

• B.

8

• C.

2

• D.

64

A. 16
Explanation
When n = 4, the value of S is equal to 16.

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• 7.

### When n = 5, what is S equal to?

• A.

10

• B.

25

• C.

3

• D.

125

B. 25
Explanation
When n = 5, the value of S is equal to 25.

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• 8.

### When n = 9, what is S equal to?

• A.

81

• B.

18

• C.

7

• D.

27

A. 81
Explanation
When n = 9, the value of S can be calculated by squaring n. So, S = 9^2 = 81.

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• 9.

• A.

100

• B.

1000

• C.

8

• D.

20

A. 100
• 10.

### When n = 121, what is S equal to?

• A.

40.3

• B.

102

• C.

60.5

• D.

11

D. 11
Explanation
When n = 121, the value of S is equal to 11.

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• Current Version
• Mar 18, 2023
Quiz Edited by
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• Jul 12, 2018
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