Question

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

Answer 1

• 7

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.