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