MathDB

14

Part of 2019 India PRMO

Problems(2)

Smallest Prime and Perfect Square of a smallest relation

Source:

8/11/2019
Find the smallest positive integer n≥10n \geq 10 such that n+6n + 6 is a prime and 9n+79n + 7 is a perfect square.
primePerfect Squarerelation
Circle in Real Plane

Source: PRMO Leg 2 P14

8/25/2019
Let R\mathcal{R} denote the circular region in the xy−xy-plane bounded by the circle x2+y2=36x^2+y^2=36. The lines x=4x=4 and y=3y=3 divide R\mathcal{R} into four regions Ri , i=1,2,3,4\mathcal{R}_i ~ , ~i=1,2,3,4. If ∣Ri∣\mid \mathcal{R}_i \mid denotes the area of the region Ri\mathcal{R}_i and if ∣R1∣>\mid \mathcal{R}_1 \mid > ∣R2∣>\mid \mathcal{R}_2 \mid > ∣R3∣>\mid \mathcal{R}_3 \mid > ∣R4∣\mid \mathcal{R}_4 \mid , determine ∣R1∣\mid \mathcal{R}_1 \mid −- ∣R2∣\mid \mathcal{R}_2 \mid −- ∣R3∣\mid \mathcal{R}_3 \mid ++ ∣R4∣\mid \mathcal{R}_4 \mid .
algebraPRMO