LIC AAO Model Paper 6

Question : 57 of 160

Marks: +1, -0

The prime number 1999 can be written as

a^2 - b^2

where a and b are natural numbers. Then the value of

a^2 + b^2

Solution:

a^2b^2

= 1999
⇒ (a + b) (a- b) = 1999
⇒ (1000 + 999) (1000-999)= 1999
∴

a^2+b^2

(1000)^2+(999)^2

= 1000000 + 998001
= 1998001

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