If $6^{83} + 8^{83}$ is divided by $49,$ then the remainder is

35

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

5

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $35$
$6^{83} + 8^{83} = (1 + 7)^{83} + (7 - 1)^{83}$
$= (1 + 7)^{83} - (1 - 7)^{83}$
$= 2 [^{83} C_{1} \cdot 7 +^{83} C_{3} \cdot 7^{3} + \dots +^{83} C_{83} \cdot 7^{83}]$
$= (2 \cdot 7 \cdot 83) + 49 I,$ where $I$ is an integer.
$2 \times 7 \times 83 = 1162$
$\frac{1162}{49} = 23 \frac{35}{49}$
$∴$ Remainder is $35.$

Suggest Corrections

Similar questions

\frac{6^{83} + 8^{83}}{49}

22^{3} + 23^{3} + 24^{3} + . . . . . . . . . + 88^{3}

22^{3} + 23^{3} + 24^{3} + \dots + 87^{3} + 88^{3}

6^{83} + 8^{83}

49,

The remainder obtained when $49^{49} + 51^{24}$ is divided by 25 is

Join BYJU'S Learning Program