IS THIS POSSIBLE

P. Q .R =19(P+R)

HERE P, Q, R are distinct prime . find P, Q, R ????

NOTE - here P .Q .R means P multiplied by Q and R. means P. Q. R is not a 3 digit no.

#NumberTheory

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Comments

ya you are correct but if they are not distinct primes then this is possible values are 2, 2 19

Jai Gupta - 6 years, 8 months ago

If PQR = 19(P+R) then one of P, Q and R is 19. If Q=19 then P+R=PR which isn't possible for distinct primes. If P=19 (chosen without loss of generality), 19+R = QR. R must be odd, as 19+2 =21 which is not prime, so 19+R is even. As 19+R = QR, QR is even, Q is even, Q is 2. But the only solution to 19+R=2R is R=19 which, again, leads to P, Q and R not being distinct.

So... no. It isn't possible.

James Moors - 6 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$