Question 73
a) For which positive integer $l$ there exists a pair of positive integers $(m, n)$, which consist of no more than $l$ digits, have different last digits and which satisfy the condition: the last $l$ digits of $m^2$ form the number $n$, and analogously, the last $l$ digits of $n^2$ form number $m$ (discarding any zeros that the last $l$ digits may begin with).
b) For which positive integer $l$ there exists a pair of positive integers $(m, n)$, which consist of no more than $l$ digits, have different last digits and which satisfy the condition: the last $l$ digits of $m^3$ form the number $n$, and analogously, the last $l$ digits of $n^3$ form number $m$ (discarding any zeros that the last $l$ digits may begin with).
b) For which positive integer $l$ there exists a pair of positive integers $(m, n)$, which consist of no more than $l$ digits, have different last digits and which satisfy the condition: the last $l$ digits of $m^3$ form the number $n$, and analogously, the last $l$ digits of $n^3$ form number $m$ (discarding any zeros that the last $l$ digits may begin with).