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p-Z-given-u-14p-3-v-5p-1-E-87x-31y-2-we-have-also-the-line-D-87x-31y-2-1-show-that-u-and-v-are-primes-between-them-i-mean-the-don-t-have-any-common-divisor-excepted-1-and-1-2-dedu




Question Number 122647 by mathocean1 last updated on 18/Nov/20
p ∈ Z. given:  u=14p+3 ; v=5p+1,  (E):87x+31y=2 ; we have   also the line (D): 87x−31y=2  1)show that u and v are primes  between them.(i mean the   don′t have any common divisor   excepted 1 and −1.)  2)deduct that 87 and 31 are  primes between them.  3)Solve (E).  4)Determinate points (x;y)∈ (D)   which that their cordonnates  x;y ∈ N and x≤100
$${p}\:\in\:\mathbb{Z}.\:{given}: \\ $$$${u}=\mathrm{14}{p}+\mathrm{3}\:;\:{v}=\mathrm{5}{p}+\mathrm{1}, \\ $$$$\left({E}\right):\mathrm{87}{x}+\mathrm{31}{y}=\mathrm{2}\:;\:{we}\:{have}\: \\ $$$${also}\:{the}\:{line}\:\left({D}\right):\:\mathrm{87}{x}−\mathrm{31}{y}=\mathrm{2} \\ $$$$\left.\mathrm{1}\right){show}\:{that}\:{u}\:{and}\:{v}\:{are}\:{primes} \\ $$$${between}\:{them}.\left({i}\:{mean}\:{the}\:\right. \\ $$$${don}'{t}\:{have}\:{any}\:{common}\:{divisor}\: \\ $$$$\left.{excepted}\:\mathrm{1}\:{and}\:−\mathrm{1}.\right) \\ $$$$\left.\mathrm{2}\right){deduct}\:{that}\:\mathrm{87}\:{and}\:\mathrm{31}\:{are} \\ $$$${primes}\:{between}\:{them}. \\ $$$$\left.\mathrm{3}\right){Solve}\:\left({E}\right). \\ $$$$\left.\mathrm{4}\right){Determinate}\:{points}\:\left({x};{y}\right)\in\:\left({D}\right)\: \\ $$$${which}\:{that}\:{their}\:{cordonnates} \\ $$$${x};{y}\:\in\:\mathbb{N}\:{and}\:{x}\leqslant\mathrm{100} \\ $$$$ \\ $$

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