Type of numbers

Number Theory Level 3

$A=\{a_{1},a_{2},a_{3},\ldots \}$

Given each number of the set $A$ is a whole number and each number of the set $A$ can be represented as a difference of squares of two consecutive whole numbers. Then which type of numbers are there in set $A$ ?

None of the above prime irrational odd complex even

1 solution

Shivamani Patil
Jun 7, 2015

Each element can be represent as $(x+1)^{2}-(x)^{2}=2x+1$ .

Which implies each element of set $A$ is odd because odd numbers are of form $2n+1$ for some $n$ .

Right.You stated it very simply and elegantly.

Siddharth Singh - 6 years ago

Thank you. Nice problem.

shivamani patil - 6 years ago

Type of numbers

1 solution

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