Find the largest value ( n &#x2265;<!-- ≥ --> 0 ) and for that that n find a and d in th

Yahir Crane

Yahir Crane

Answered question

2022-06-26

Find the largest value ( n 0 ) and for that that n find a and d in the following equation (also a and d are positive integers):
4020 = ( 2 a + n d + 1 ) n

Answer & Explanation

grcalia1

grcalia1

Beginner2022-06-27Added 23 answers

We know that n must be a prime factor or product of the prime factors ( 3 , 4 , 5 , 67 ). Clearly if a and d are positive integers 2 a + n d + 1 > n. So if n is divisible by 67 then ( 2 a + n d + 1 ) n > 67 2 > 4020 hence n must be at most 3 × 4 × 5. We see that by setting n = 60 , a = 3 , d = 1 we have a solution, so n = 60 is the maximum n

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