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Help ill give you 25 points

Find p if p doesnt equal 1 and is a natural number and
3n+2 is divisible by p
8n+3 is divisible by p

Respuesta :

mhanifa

Answer:

  • 7

Step-by-step explanation:

3n+2 is divisible by p:

  • 3n + 2 = px

8n+3 is divisible by p:

  • 8n + 3 = py

Solve each equation for n:

  • n = (px - 2)/3
  • n = (py - 3)/8

Eliminate n and solve for p:

  • (px - 2)/3 = (py - 3)/8
  • 8(px - 2) = 3(py - 3)
  • 8px - 16 = 3py - 9
  • 8px - 3py = 7
  • p = 7/(8x - 3y)

As we see p could get 1 or 7 as natural number. Since 1 is excluded, the only solution is 7, and 8x - 3y must equal to 1.

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