Mathcounts National Sprint Round Problems And Solutions May 2026

The factors could be -1 and -prime? But (n>0) gives positive factors. So no solutions? That can’t be – the problem expects a sum.

Now 289 = 17^2. Positive integer factor pairs: (1,289), (17,17), (289,1). Case 1: 3a-17=1 → a=6, then 3b-17=289 → b=102 → sum=108. Case 2: 3a-17=17 → a=34/3 no. Case 3: 3a-17=289 → a=102, then b=6 → same sum 108. Also negative factors? a,b positive so 3a-17> -? Actually if a=1, 3-17=-14, product with negative to get 289, but then b negative. So only positive pairs. Mathcounts National Sprint Round Problems And Solutions

(\boxed108)

Coordinates: Let A=(0,0), B=(8,0), C=(8,15), D=(0,15). E on CD: C(8,15) to D(0,15) is horizontal, so y=15. CE=5 means from C (x=8) to E (x=3) → E=(3,15). The factors could be -1 and -prime