The smallest positive integer such that if we divide it by three, the remainder is 2. if we divide it by five, the remainder is 3. if we divide it by seven, the remainder is 2.

DofotheroU
2021-05-06
Answered

To find:

The smallest positive integer such that if we divide it by three, the remainder is 2. if we divide it by five, the remainder is 3. if we divide it by seven, the remainder is 2.

The smallest positive integer such that if we divide it by three, the remainder is 2. if we divide it by five, the remainder is 3. if we divide it by seven, the remainder is 2.

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Ayesha Gomez

Answered 2021-05-08
Author has **104** answers

Suppose the required smallest positive integer is x.

Then by the given information, there are congruence equations

The congruence

So the number x is one of the numbers from the following list:

2,5, 8, 11, 14, 17, 20, 23, 26,29,...

Similarly, the congruence

So the number x is one of the numbers from the following list:

3,8, 13, 18, 23, 28, 33, 38,43,...

The congruence

So the number x is one of the numbers from the following list:

2,9, 16,23, 30, 37,44,...

The smallest number that is found in the above three lists is 23.

So the smallest number that solves the congruences

Final Statement:

The smallest positive integer with the given conditions is 23.

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To determine:To prove:The congruency of $\mathrm{\angle}PBC\stackrel{\sim}{=}\mathrm{\angle}PBD$ .

Given information:

The following information has been given

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Given information:

The following information has been given

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Having the equation

${a}^{T}x=b$

where $a$,$a,x\in {\mathbb{R}}^{n}$, $b$ is a number. Can I solve $x$ in terms of $a$,$b$?

Ultimate goal is to find the maximum of

$\frac{1}{2}{x}^{T}Px$

given ${a}^{T}x=b$, where $P$ is a symmetric positive definite matrix.

${a}^{T}x=b$

where $a$,$a,x\in {\mathbb{R}}^{n}$, $b$ is a number. Can I solve $x$ in terms of $a$,$b$?

Ultimate goal is to find the maximum of

$\frac{1}{2}{x}^{T}Px$

given ${a}^{T}x=b$, where $P$ is a symmetric positive definite matrix.

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Solve below somewhat symmetric equations:

x, y, z subject to

${x}^{2}+{y}^{2}-xy=3$

${(x-z)}^{2}+{(y-z)}^{2}-(y-z)(x-z)=4$

${(x-z)}^{2}+{y}^{2}-y(x-z)=1$

$x,y,z\in {R}^{+}$

x, y, z subject to