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

Modern Puzzles by Henry Ernest Dudeney: $23$

De Morgan and Another

Augustus de Morgan, 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 De Morgan and Jenkins were respectively born?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Age and Kinship Puzzles: $23$. -- De Morgan and Another
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Age Puzzles: $34$. De Morgan and Another