All Questions Topic List
Arithmetic Questions
Previous in All Question Next in All Question
Previous in Arithmetic Next in Arithmetic
Question Number 128012 by mathocean1 last updated on 03/Jan/21
showthat∀n∈N,12divisen2(n4−1)
Answered by MJS_new last updated on 03/Jan/21
n=2k⇒2∣n⇒4∣n2n=2k+1⇒n4−1=8k(k−1)(2k2−2k+1)⇒⇒4∣n4−1⇒4∣n2(n4−1)n=3k⇒3∣n2n=3k+1⇒n4−1=3k(3k+2)(9k2+6k+2)⇒⇒3∣n4−1n=3k+2⇒n4−1=3k(k+1)(3k+1)(9k2+12k+5)⇒⇒3∣n4−1⇒3∣n2(n4−1)⇒12∣n2(n4−1)
Terms of Service
Privacy Policy
Contact: info@tinkutara.com