Question

25¹⁹⁰ - 19¹⁹⁰ - 8¹⁹⁰ + 2¹⁹⁰ is divisible by

• A. both 14 and 34
• B. 14 but not 34
• C. 34 but not 14
• D. neither 14 nor 34

Answer 1

The Correct Option is C

Given:
\( 25^{190} - 8^{190} \) is divisible by \( 25 - 8 = 17 \)
\( 19^{190} - 2^{190} \) is divisible by \( 19 - 2 = 17 \)
\( 25^{190} - 19^{190} \) is divisible by \( 25 - 19 = 6 \)
\( 8^{190} - 2^{190} \) is divisible by \( 8 - 2 = 6 \)

Now, we calculate the least common multiple (L.C.M.) of 1746:
The L.C.M. of 1746 is 34.

Therefore, the number is divisible by 34 but not by 14.