Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

Show that (n^2-1) is divisible by 2 if n is an odd positive integer?
Asked by manhas | 08 Apr, 2017, 11:31: PM
answered-by-expert Expert Answer
Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some integer p.
 
Let n = 4p+ 1
 
(n2 – 1) = (4p + 1)2 – 1 = 16p2 + 8p + 1 = 16p2 + 8p = 8p (2p + 1)
⇒ (n2 – 1) is divisible by 2, since 8 is divisible by 2.
 
(n2 – 1) = (4p + 3)2 – 1 = 16p2 + 24p + 9 – 1 = 16p2 + 24p + 8 = 8(2p2 + 3p + 1)
⇒ (n2 – 1) is divisible by 2, since 8 is divisible by 2.
 
Therefore, n2– 1 is divisible by 2 if n is an odd positive integer.
Answered by Rebecca Fernandes | 27 Nov, 2017, 02:35: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
the HCF of 867 and 255 is
Asked by sharmapoonam0698 | 31 Dec, 2023, 04:16: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
What is the HCF of the numbers 440 and 1782
Asked by pak420280 | 25 Sep, 2023, 07:51: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Find the LCM of 2³ × 3² and 2² × 3³.
Asked by susrisangita792 | 22 Apr, 2023, 09:14: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
Find the smallest number which when divided by 45, 30, 60 having remainder 5 in each case.
Asked by susrisangita792 | 20 Apr, 2023, 08:07: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
a number n when divides by 16 gives the reminder 5 ______ is the reminder when the same number divide by 8
question image
Asked by abdulbasitoo798 | 20 Jan, 2023, 08:15: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
find log27base3
Asked by ambatisonu123 | 13 Dec, 2021, 09:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
what is the meaning of uklid division
Asked by akhilesh.k19857 | 12 Nov, 2021, 09:37: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
what do you mean by h.c.f
Asked by yedurukumari906 | 12 Nov, 2021, 05:09: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
use euclid division algorithm to find hCf of . 196and38220
Asked by diya1213 | 04 Oct, 2021, 08:53: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
When the HCF (420, 130) is expressed as a linear combination of 420 and 130 i.e. HCF (420, 130) = 420x + 130y, the values of x and y satisfying the above relation are:  (a)x= 3, y = 1  (c) x = 4, y = -13  (b) x=-4, y = 13  (d) x = 2, y = 3​
Asked by adnankhan7860098 | 21 Sep, 2021, 06:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×