Number Theory – Page 40

Question-24944

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Question Number 24944 by soufiane zarik last updated on 29/Nov/17 Commented by prakash jain last updated on 30/Nov/17 $x = n + f 0 ⩽ f < 1, n \in Z, n ⩾ 0$ $[{(n + f)}^{2}] = {[n + f]}^{2}$ $$\Rightarrow\left[{n}^{\mathrm{2}} +\mathrm{2}{nf}+{f}^{\mathrm{2}}…

For-any-positive-integer-n-n-is-the-number-of-its-factors-Prove-i-1-n-i-i-1-n-n-i-

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Question Number 90470 by Asif Hypothesis last updated on 23/Apr/20 $F o r a n y p o s i t i v e i n t e g e r n, τ (n) i s t h e n u m b e r o f i t s f a c t o r s$ $P r o v e,$ $\sum_{i = 1}^{n} τ (i) = \sum_{i = 1}^{n} ⌊ n / i ⌋$ Terms of Service Privacy…

Find-the-cube-root-of-one-Hence-show-that-the-sum-of-the-root-is-equal-to-zero-

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Question Number 155571 by peter frank last updated on 02/Oct/21 $Find the cube root of one . Hence$ $show that the sum of the root is$ $equal to zero$ Answered by JDamian last updated on 02/Oct/21 $${z}^{\mathrm{3}}…

A-four-digit-whole-number-is-interesting-if-the-number-formed-by-the-leftmost-two-digits-is-twice-as-large-as-the-number-formed-by-the-rightmost-two-digits-for-example-2010-is-interesting-1-find-t

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Question Number 89878 by malwaan last updated on 19/Apr/20 $A f o u r_d i g i t w h o l e n u m b e r$ $i s i n t e r e s t i n g i f t h e n u m b e r$ $f o r m e d b y t h e l e f t m o s t t w o$ $d i g i t s i s t w i c e a s l a r g e a s t h e$ $n u m b e r f o r m e d b y t h e$ $r i g h t m o s t t w o d i g i t s .$ $(f o r e x a m p l e 2010 i s i n t e r e s t i n g)$ $$\mathrm{1}\:\:\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{largest}}\:\boldsymbol{{whole}}\:\boldsymbol{{number}} \…

Find-the-minimum-possible-least-common-multiple-lcm-of-twenty-not-necessarily-distinct-natural-numbers-whose-sum-is-801-

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Question Number 24324 by Tinkutara last updated on 15/Nov/17 $Find the minimum possible least$ $common multiple (lcm) of twenty (not$ $necessarily distinct) natural numbers$ $whose sum is 801 .$ Commented by Tinkutara last updated on 16/Nov/17…

n-0-1-n-2n-1-3-

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Question Number 155133 by amin96 last updated on 25/Sep/21 $\underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{{(2 n + 1)}^{3}} = ?$ Answered by mnjuly1970 last updated on 26/Sep/21 $$\:\:\:\frac{\pi^{\:\mathrm{3}} }{\mathrm{32}}…

Find-the-last-2-digits-from-20-17-17-20-

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Question Number 23612 by Joel577 last updated on 02/Nov/17 $Find the last 2 digits from$ $20^{17} + 17^{20}$ Commented by Rasheed.Sindhi last updated on 02/Nov/17 $$\mathrm{20}^{\mathrm{17}} =\left(\mathrm{2}×\mathrm{10}\right)^{\mathrm{17}} =\mathrm{2}^{\mathrm{17}}…

how-many-positive-x-10-000-integers-are-such-that-2-x-x-2-is-divisible-by-7-

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Question Number 154672 by talminator2856791 last updated on 20/Sep/21 $how many positive x ⩽ 10 000 integers are$ $such that 2^{x} - x^{2} is divisible by 7 ?$ Answered by MJS_new last updated…

Prove-that-3k-2-is-not-perfect-square-for-all-k-0-1-2-3-

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Question Number 23269 by Rasheed.Sindhi last updated on 28/Oct/17 $P rove that$ $3 k + 2 is not perfect square for$ $all k \in {0, 1, 2, 3, \dots} .$ Answered by Tinkutara last updated on 28/Oct/17 $${Any}\:{number}\:{can}\:{be}\:{written}\:{as}\:\mathrm{3}{p}, \…

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}}…

Category: Number Theory