Coloring problems: ISI MMA 2018 Question 10

Coloring problems: ISI MMA 2018 Question 10

Understand the problem A new flag of ISI club is to be designed with 5 vertical strips using some or all the four colours : green , naroon , red and yellow . In how many ways this can be done  so that no two adjacent strips have the same colour ?  Source of the...
Repunits in arbitrary bases

Repunits in arbitrary bases

Understand the problem find all integers  such us  is a perfect square. Source of the problem New Zealand team training 2004 Topic Number Theory Difficulty Level Medium Suggested Book An Excursion in Mathematics Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you...
Argentina TST 2005

Argentina TST 2005

Understand the problem Let  and  be positive integers greater than , with  being a prime. Show that if  divides  and  divides , then  is a perfect square. Source of the problem Argentina TST 2005 Topic Number Theory Difficulty Level Easy Suggested Book An Excursion in...