**7**

*Peculiarity of the number 65*

- The number 65 is the "smallest number" which can be expressed as the
sum of two different squares in two different ways-

i.e., 65= 12 +82 = 42+72. - The number 65 is the "smallest number " which can be expressed as the
sum of two different cubes of positive integers-

i.e., 65= 13+43. - The number 65 is the "smallest number" which can be expressed as the sum
of squares of two different cubic number as well as the sum of cubes of
two different square numbers-

i.e.,65 = 12+82 where 1 & 8 are cubic numbers.

= 13+43 where 1 & 4 are square numbers - 4. The number 65 also gives a perfect square on adding or subtracting
its reverse from it-

i.e., 65+56 =121= 112

65-56 = 9 = 32

**Moumita Pal
[Epsilon]**

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