Question: Augustus De Morgan, the mathematician, who died in 1871, used to boast that he was x years old in the year x2• Jasper Jenkins, wishing to improve on this, told me in 1925 that he was a2 + b2 in a4 + b4 ; that he was 2m in the year 2m2; and that he was 3n years old in the year 3n4• Can you give the years in which De Morgan and Jenkins were respectively born?
Answer: De Morgan was born in 1806. When he was 43, the year was the square of his age-1849. Jenkins was born in 1860. He was 52 + 62 (61) in the year 54 + 64 (1921). Also he was 2 X 31 (62) in the year 2 X 312 (1922). Again, he was 3 X 5 (15) in the year 3 X 54 (1875).
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