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let a,b,c be positive whole numbers. Where a>c. If both a-b and c-b are prime. and a+c = 2019. What is the greatest value of b

 
 Jan 22, 2023
 #1
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The greatest value of b is 1992.

 
 Jan 22, 2023
 #2
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Try these:

 

a=1010

b=1007

c=1009

 

a + c =1010  +  1009 = 2019  and a > c

a  -  b=1010  -  1007 = 3 - is a prime

c  -  b=1009  -  1007 =2 - is a prime

 

The largest b in this solution =1007

 
 Jan 23, 2023

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