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chubhunter [2.5K]
2 years ago
6

in base ten, the two-digit prime N is 45 more than the number formed by reversing the digits of N, find all the possible values

of N.
Mathematics
1 answer:
Drupady [299]2 years ago
6 0
Let N=10x+y, so that x is the digits in the tens place and y is the digit in the ones place. (Clearly x\neq0.)

10x+y=45+10y+x\implies 9x-9y=45\implies x-y=5

There are five possible two digits integers that satisfy this relation:

x=5,y=0\implies N=50
x=6,y=1\implies N=61
x=7,y=2\implies N=72
x=8,y=3\implies N=83
x=9,y=4\implies N=94

But the first, third, and fifth candidates are even, so they are not prime. The remaining are prime, however, so N=61 or N=83.
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