Number Theory – Page 66

prove-that-5555-2222-2222-5555-is-divisible-by-7-

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Question Number 772 by malwaan last updated on 12/Mar/15 $p r o v e t h a t$ $5555^{2222} + 2222^{5555}$ $i s d i v i s i b l e b y 7$ Commented by 123456 last updated on 10/Mar/15…

Prove-that-product-of-any-n-consecutive-integers-is-divisiblr-by-n-

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Question Number 769 by rishabh last updated on 09/Mar/15 $P r o v e t h a t p r o d u c t o f a n y n c o n s e c u t i v e i n t e g e r s$ $i s d i v i s i b l r b y n!$ Commented by 123456 last updated on 09/Mar/15 $n (n + 1) \cdot \cdot \cdot (2 n - 1)$ Answered…

List-all-primes-p-for-which-p-2-and-p-4-are-also-primes-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 765 by prakash jain last updated on 09/Mar/15 $List all primes p for which p + 2 and p + 4$ $are also primes .$ Answered by rishabh last updated on 09/Mar/15 $p = 3 is the only such number .$ $$\mathrm{Let}\:\mathrm{us}\:\mathrm{assume}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{prime}\:{p}>\mathrm{3}.…

Determine-the-number-of-integral-factors-of-105840-excluding-1-and-105840-

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Question Number 751 by 112358 last updated on 06/Mar/15 $D e t e r m i n e t h e n u m b e r o f i n t e g r a l$ $f a c t o r s o f 105840, e x c l u d i n g 1$ $a n d 105840 .$ Answered by prakash jain last…

Prove-that-for-p-q-r-N-lcm-p-q-r-gcd-p-q-r-p-q-r-gcd-p-q-gcd-q-r-gcd-r-p-

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Question Number 66275 by Rasheed.Sindhi last updated on 12/Aug/19 $P r o v e t h a t f o r p, q, r \in N$ $\frac{lcm (p, q, r)}{\gcd (p, q, r)} = \frac{p \times q \times r}{\gcd (p, q) \times \gcd (q, r) \times \gcd (r, p)}$ Commented by Prithwish sen last updated on 12/Aug/19 $$\mathrm{p}=\mathrm{nn}_{\mathrm{1}} \mathrm{n}_{\mathrm{2}} \mathrm{x},\mathrm{q}=\mathrm{nn}_{\mathrm{2}}…

Prove-by-induction-on-n-for-n-2-u-n-2-3-n-1-for-the-sequence-u-n-defined-by-the-recurrence-relation-u-1-1-

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Question Number 591 by 112358 last updated on 04/Feb/15 $P r o v e b y i n d u c t i o n o n n, f o r n ⩾ 2,$ $u_{n} ⩾ 2^{3^{n - 1}}$ $f o r t h e s e q u e n c e {u_{n}} d e f i n e d b y$ $t h e r e c u r r e n c e r e l a t i o n$ $u_{1} = 1$ $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{u}_{{n}+\mathrm{1}} =\left({u}_{{n}}…

xy-6-x-y-x-2-y-2-325-x-y-

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Question Number 572 by kth last updated on 29/Jan/15 $x y = 6 (x + y)$ $x^{2} + y^{2} = 325$ $x = ?$ $y = ?$ Answered by prakash…

Determine-the-complex-number-z-such-that-z-2-tanx-icosx-in-the-form-z-p-ik-p-k-R-

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Question Number 558 by 112358 last updated on 26/Jan/15 $D e t e r m i n e t h e c o m p l e x n u m b e r$ $z s u c h t h a t z^{2} = t a n x + i c o s x,$ $i n t h e f o r m z = p + i k, p, k \in R .$ Answered by prakash jain last updated…

proof-that-log-2-3-is-irrational-

Tinku Tara June 3, 2023 Number Theory 0 Comments

Question Number 552 by 123456 last updated on 25/Jan/15 $p r o o f t h a t \log_{2} 3 i s i r r a t i o n a l$ Answered by prakash jain last updated on 25/Jan/15 $Let us say \log_{2} 3 is rational, then$ $$\mathrm{log}_{\mathrm{2}}…

how-many-digits-are-in-periodic-part-of-1-60-30-

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Question Number 548 by 123456 last updated on 25/Jan/15 $h o w m a n y d i g i t s a r e i n p e r i o d i c p a r t$ $o f \frac{1}{60^{30}}$ Answered by prakash jain last updated on 25/Jan/15 $$\frac{\mathrm{1}}{\left(\mathrm{60}\right)^{\mathrm{30}} }=\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{30}}…

Category: Number Theory