a 2 − b 2 = ? a^2 - b^2 = \boxed{?}

Number Theory Level 1

True or false:

The positive difference between the squares of any two consecutive integers is always an odd number

False True

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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2 solutions

Naren Bhandari
Nov 12, 2017

a 2 − b 2 = ( a − b ) ( a + b ) = a + ( a − 1 ) c c c c a − b = 1 , a > b = 2 a − 1 \begin{aligned} a^2-b^2& = (a-b)(a+b) \\& = a+(a-1) \phantom{cccc} a-b = 1, a> b \\& = 2a-1 \end{aligned}

So the statement is true.

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How to get that statement box ? Can you help me ? :)

Naren Bhandari - 3 years, 7 months ago

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> Write anything! \text{> Write anything!}

appear as

Write anything!

Munem Shahriar - 3 years, 7 months ago

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Thank you ! 😊

Naren Bhandari - 3 years, 6 months ago
Saksham Jain
Nov 12, 2017

(A+1)²-A²=> (A+1+A)(1)==> 2A+1

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