Find-the-sum-of-the-last-ten-digits-5-23-2-2022-2023-

Question Number 184877 by Shrinava last updated on 13/Jan/23

Find the sum of the last ten digits :

5^{23} \cdot 2^{2022} - 2023

Answered by Rasheed.Sindhi last updated on 14/Jan/23

5^{23} \cdot 2^{2022} - 2023

5^{23} \cdot 2^{23} \cdot 2^{1999} - 2023

2^{1999} . 10^{23} - 2023

2^{1999} \cdot 1 \underset{23 z e r o s}{\underset{⏟}{00000 \dots 0000}} - 2023

= \dots a \underset{23 z e r o e s}{\underset{⏟}{000 \dots 00}} - 2023

a, t h e 24 t h d i g i t f r o m r i g h t, i s a

n o n - z e r o d i g i t

W e n e e d b o r r o w i n o r d e r t o s u b t r a c t 2023

A f t e r b o r r o w i n g :

L a s t 24 d i g i t s w i l l b e c h a n g e d :

\overset{―}{(a - 1) \underset{⏟}{99999 \dots 9 9 9} (10)}

\underline{- 2 0 2 3}

\underset{L a s t 23 n u m b e r s}{\underset{⏟}{9 9 9 \dots 9 9 9 7 9 7 7}}

L a s t t e n d i g i t s : 9999997977

Commented by Shrinava last updated on 15/Jan/23

thank you dear professor cool