Number Theory – Page 41

m-2-n-2-2mn-m-2-n-2-is-pythagorean-triplet-for-all-m-n-N-This-can-be-proved-easily-Is-the-vice-versa-of-the-statement-is-also-true-I-E-If-for-a-b-c-N-a-2-b

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Question Number 23105 by Rasheed.Sindhi last updated on 26/Oct/17 $(∣ m^{2} - n^{2} ∣, 2 mn, m^{2} + n^{2}) is pythagorean$ $triplet for all m, n \in N . This can be$ $proved easily . Is the vice versa of$ $the statement is also true ?$ $I - E$ $$\mathrm{If}\:\:\mathrm{for}\:\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{N}\:,\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}}…

The-value-of-n-0-3-n-2-n-x-n-1-n-n-2-n-1-is-a-1-2-n-0-2-n-x-n-n-b-1-2-n-0-3-n-2-n-1-n-x-n-n-c-1-2-n-0-2-n-x-n-1-

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Question Number 153916 by EDWIN88 last updated on 12/Sep/21 $T h e v a l u e o f \underset{n = 0}{\sum^{\infty}} \frac{(3_{n}) (2_{n}) x^{n}}{(1_{n}) n!} β (2, n + 1) i s$ $a . \frac{1}{2} \underset{n = 0}{\sum^{\infty}} (2_{n}) \frac{x^{n}}{n!}$ $${b}.\:\frac{\mathrm{1}}{\mathrm{2}}\underset{{n}=\mathrm{0}} {\overset{\infty}…

Question-88261

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Question Number 88261 by ar247 last updated on 09/Apr/20 Answered by Joel578 last updated on 09/Apr/20 $u \equiv v (\mod m) \Rightarrow u - v = m x, x \in Z$ $(1) u = m x + v$ $Since gcf (v, m) divides both v and m, it also divides u,$ $hence gcf (v, m) divides gcf (u, m)$ $$\Rightarrow\:\mathrm{gcf}\left({v},{m}\right)\:\mid\:\mathrm{gcf}\left({u},{m}\right)…

For-each-positive-integer-n-define-a-n-20-n-2-and-d-n-gcd-a-n-a-n-2-Find-the-set-of-all-values-that-are-taken-by-d-n-

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Question Number 22635 by Rasheed.Sindhi last updated on 21/Oct/17 $For each positive integer n, define$ $a_{n} = 20 + n^{2}, and d_{n} = \gcd (a_{n}, a_{n + 2}) .$ $Find the set of all values that are$ $taken by d_{n} .$ $$ \…

For-each-positive-integer-n-define-a-n-30-n-2-and-d-n-gcd-a-n-a-n-1-Find-the-set-of-all-values-that-are-taken-by-d-n-and-show-by-examples-that-each-of-these-values-are-attained-

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Question Number 22625 by Rasheed.Sindhi last updated on 21/Oct/17 $For each positive integer n define$ $a_{n} = 30 + n^{2}, and d_{n} = \gcd (a_{n}, a_{n + 1}) .$ $Find the set of all values that are$ $taken by d_{n} and show by examples$ $$\mathrm{that}\:\mathrm{each}\:\mathrm{of}\:\mathrm{these}\:\mathrm{values}\:\mathrm{are}\:\mathrm{attained}. \…

Question-88050

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Question Number 88050 by Sahil vampire last updated on 08/Apr/20 Commented by mr W last updated on 08/Apr/20 $i f o u n d t h e r e i s o n l y o n e s u c h n u m b e r :$ $588 2353$ $$\mathrm{588}^{\mathrm{2}} +\mathrm{2353}^{\mathrm{2}} =\mathrm{588}\:\mathrm{2353}…

Is-there-a-formula-to-calculate-i-1-n-1-i-2-interms-of-n-

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Question Number 88000 by jdmath last updated on 07/Apr/20 $I s t h e r e a f o r m u l a t o c a l c u l a t e$ $\underset{i = 1}{\sum^{n}} \frac{1}{i^{2}}$ $i n t e r m s o f n . . ?$ Commented by abdomathmax last…

Given-a-set-consisting-of-22-integer-A-a-1-a-2-a-11-Show-that-exist-subset-of-S-with-properties-1-for-every-i-1-2-3-11-have-least-one-between-a-i-or-a-i-element-of-S-2-the

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Question Number 153458 by liberty last updated on 07/Sep/21 $G i v e n a s e t c o n s i s t i n g o f 22 i n t e g e r$ $A = {\pm a_{1}, \pm a_{2}, \dots, \pm a_{11}} . S h o w t h a t$ $e x i s t s u b s e t o f S w i t h p r o p e r t i e s$ $(1) f o r e v e r y i = 1, 2, 3, \dots, 11$ $h a v e l e a s t o n e b e t w e e n a_{i} o r - a_{i}$ $$\:{element}\:{of}\:{S} \…

Question-22372

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Question Number 22372 by Rasheed.Sindhi last updated on 16/Oct/17 Commented by Rasheed.Sindhi last updated on 16/Oct/17 $Question asked by Mr . Tinkutara .$ $reposted for answer .$ Commented by Tinkutara last…

Question-87785

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Question Number 87785 by Sayantan chakraborty last updated on 06/Apr/20 Terms of Service Privacy Policy Contact: info@tinkutara.com

Category: Number Theory