Question

If 7¹⁰³ is divided by 25, then the remainder is _____.​

Answer 1

Answer:

7103

=7102(7)

=7(49)51

=7(50−1)51

=7(5051−51(50)50+(51)(25)(50)49...+(51)(50)−1)

=7(50k−1)

=350k−7

=350k+25−25−7

=(350k−25)+25−7

=(350k−25)+18 ...(a)

When 'a' is divided by 25 it leaves a remainder 18.

Hence, when 7103 is divided by 25, it leaves a remainder 18.

Answer 2

$7 {}^{103}$

$= 7 {}^{102} (7)$

$= 7(49) {}^{51}$

$= 7(50 - 1) {}^{51}$

$= 7(50 {}^{51} - 51(50) {}^{50} + (51)(25)(50) {}^{49} .... +$

$(51)(50) - 1)$

$= 7(50k - 1)$

$= 350k - 7$

$= 350k + 25 - 25 - 7$

$= (350k - 25) + 25 - 7$

$= (350k - 25) + 18....(a)$

$when \: 'a' \: is \: divided \: by \: 25 \: it \: leaves \: a \: \\ remainder \: 18.$

$Hence, \: when \: 7 {}^{103} \: is \: divided \: by \: 25 , \: it \: \\ leaves \: a \: remainder \: 18.$

Step-by-step explanation:

$@BrainlyGENIUS$