## 21 Jun Few problems - 4

- Find all integers satisfying such that is a divisor of .
- Find the number of ordered pairs of positive integers which satisfy .
- The integer consists of 2017 consecutive nines. A computer calculates . How many nines does the number contain in total ?
- Let be an acute angled triangle such that . Let $D$ be a point on such that . Let be an internal point of the segment . Prove that if and only if .
- Let where 1" /> is an integer. Prove that cannot be expressed as the product of two non-constant polynomials with integer coefficients.

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#### Debashish Sharma

Assistant Professor at Gurucharan College

Dr. Debashish Sharma is an Assistant Professor in the Department of Mathematics, Gurucharan College, Silchar, Assam.

#### Latest posts by Debashish Sharma (see all)

- Few problems - 4 - June 21, 2017
- Algebra behind the scenes : Reed-Solomon Algorithm - April 29, 2017
- In memory of Prof. Jonathan Borwein - August 7, 2016
- "Mathematics Lab" - July 20, 2016
- Interview with Prof. Anatoly Vershik - February 9, 2016

## ramesh nath jogi

Posted at 21:27h, 09 Julya2+b2=