Henry Ernest Dudeney/Modern Puzzles/23 - De Morgan and Another

by : $23$

 * De Morgan and Another
 * , the mathematician, who died in $1871$, used to boast that he was $x$ years old in the year $x^2$.
 * My living friend, Jasper Jenkins, wishing to improve on this, tells me he was $a^2 + b^2$ in $a^4 + b^4$;
 * that he was $2 m$ in the year $2 m^2$;
 * and that he was $3 n$ years old in the year $3 n^4$.


 * Can you give the years in which and Jenkins were respectively born?