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Mr. Gregory White
Mr. Gregory White, Master's Degree
Category: Pre-Calculus
Satisfied Customers: 5232
Experience:  M.A., M.S. Education / Educational Administration
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How many points with positive integer coefficients are inside

Customer Question

How many points with positive integer coefficients are inside or on the right triangle with vertices (0,0) , (0,A) , (B,0) for positive integers A and B, without adding together A or B numbers?
Submitted: 1 year ago.
Category: Pre-Calculus
Expert:  Mr. Gregory White replied 1 year ago.
Hello, my name is Greg.
If nonnegative integer coefficients, the number of
such points is
(1/2)*(ab + a + b + 2 + gcd(a,b))
If meant positive integer coefficients, the number of
such points is
(1/2)*(ab - a - b + gcd(a,b))
Customer: replied 1 year ago.
Can you prove it?
Expert:  Mr. Gregory White replied 1 year ago.
Not without extensive working through the problem which would go above and beyond the price point of this question.

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