MHB Find Integer Solutions Challenge

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The challenge is to find integer pairs (p, q) satisfying the equation 1 + 1996p + 1998q = pq. By rearranging the equation, it can be expressed as (p-1998)(q-1996) = 1997^2. The solutions derived from this equation are (1, 1997^2), (1997, 1997), (1997^2, 1), along with their negative counterparts (-1, -1997^2), (-1997, -1997), and (-1997^2, -1). The prime nature of 1997 is crucial in determining the solution set. Thus, the integer solutions are fully characterized by these pairs.
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Find all pairs $(p, q)$ of integers such that $1+1996p+1998q=pq$.
 
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Hint:
[sp]What is $(p-1)(q+1)$?[/sp]
Further hint:
[sp]$1997$ is a prime number.[/sp]
 
I shall proceed differently from Opalg

Pq – 1996p – 1998q = 1

Or (p-1998)(q-1996) – 1998 * 1996 = 1

Or (p-1998)(q-1996) = 1998 * 1996 + 1 = 1997^2

We get all the solution set for (p-1998, q- 1996) to be ( 1, 1997^2), (1997,1997), ( 1997^2, 1)
(-1, - 1997^2), (-1997,- 1997), (- 1997^2, - 1) as 1997 is prime
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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