answersLogoWhite

0


Best Answer

Assuming it's a2-1 you mean.

If a2-1 is even, it can be expressed as a2-1 = 2 * t, where t is a natural number.

a2-1 = (a - 1)(a + 1) = 2 * t

You immediately see that at least one of the terms in parenthesis has to be even, and then, that actually both have to be even, because (a + 1) - (a - 1) = 2.

Therefore, you can express both of the terms as:

a - 1 = 2 * s

a + 1 = 2 *r,

which gives us:

2 * s * 2 * r = a2 - 1, simplify:

4 * r * s = a2 - 1.

Therefore, if a2-1 is even, a2-1 is also divisible by 4.

User Avatar

Wiki User

15y ago
This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: For each integer a if a2-1 is even then 4 divides a2-1?
Write your answer...
Submit
Still have questions?
magnify glass
imp
Continue Learning about Algebra
Related questions

Who is behind the A21 campaign site?

The A21 Campaign was founded by Nick and Christine Caine in 2007. See the related link for more information.


What is A21?

A21, Always 21, is an international fast-fashion brand that upholds the philosophy that "Always 21, always be yourself". A21 was found in 2013 and start to face global customers in 2021. A21 is committed to providing fashionably and high-quality products at an equitable price with the young crowds all over the world. A21 follows the global fashion trend and aims to share the young, fashionable lifestyle and active life attitude with our global customers. A21 contains women’s wear series, men’s wear series, and children’s wear series. A21 online business mainly focuses on women‘s wear and offers high quality, stylish and comfortable wear for young female customers. The online business of A21 mainly targets American, European, and Japanese customer markets.


How many sides does a21 sided figure have?

21


What is round white pill with M on one side and A21 on the other?

According to Drug.com's Pill Identifier, a round white pill imprinted with 'M' and 'A21' is Alprazolam Extended-Release, 0.5mg.


What is the distance from London tp hastings?

60 miles taking A21.


What is the total miles from rome to Alexandria italy?

600 km (373 miles) taking this route:Take A1 FIRENZE, from Roma, to A21 TORINO (at PIACENZA NORD uscita (exit)).Take A21 to Alessandria.


How far is it to Bromley UK from Southampton UK?

The shortest driving distance is 100 miles taking this route:Take M3 LONDON, from Southampton, to M25 GATWICK at J2.Take M25 to A21 BROMLEY at J4.Take A21 to Bromley.


How many miles between woking and camber sands?

About 84 miles on the M25 and A21


What are Greyhound bus ticket restrictions A21?

A21 is Advance-21, the 21-day advance-ticket purchase discount. The main restriction is that you cannot purchase a 21-day advance-ticket, then expect to change your ticket to a sooner travel date without losing the discount.


Driving distance lyon and Verona?

Take the A43 and A21 / 625 km - about 6 hours 10 mins.


How far from Fishguard to Tonbridge?

290 milesThis is the route:Follow signs to M4 from Fishguard, then take M4(E) towards CARDIFF and SWANSEA, through South Wales, across the Severn Crossing (toll) into ENGLAND, and then across to M25(S) @ J4B outside of London.Take M25 around London to A21 towards HASTINGS @ J5.Take A21 to Tonbridge.


A is a 3 x 4 matrix what is its transpostion?

If A is a 3x4 matrix with values ([a11, a12, a13, a14], [a21, a22, a23, a24], [a31, a32, a33, a34]) then its transpose AT is a 4x3 matrix values with its values changed diagonally like so, ([a11, a21, a31], [a12, a22, a32], [a13, a23, a33], [a14, a24, a34])