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Mr. Gregory White
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PreCalculus
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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:
PreCalculus
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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))
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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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