Question

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Users Jee Question Let's See Who can Solve ? Find Remainder when (13 {}^{13} + 1)(13 13 +1) is divided by 14
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Answer 1

Answer:

ɢɪᴠᴇɴ :-

13^13 +1 ɪꜱ ᴅɪᴠɪᴅᴇᴅ ʙʏ 14

ᴛᴏ ꜰɪɴᴅ :-

ꜰɪɴᴅ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ?

ꜱᴏʟᴜᴛɪᴏɴ :-

ɢɪᴠᴇɴ ɴᴜᴍʙᴇʀ ɪꜱ 13^13 +1

ɪᴛ ᴄᴀɴ ʙᴇ ᴡʀɪᴛᴛᴇɴ ᴀꜱ 13^13 + 1^13

ᴏɴ ᴄᴏᴍᴘᴀʀɪɴɢ ᴛʜɪꜱ ᴡɪᴛʜ x^ɴ + ʏ^ɴ

ᴡᴇ ʜᴀᴠᴇ ,

x = 13

ʏ = 1

ɴ = 13

ʜᴇʀᴇ , ɴ ɪꜱ ᴀɴ ᴏᴅᴅ ɴᴜᴍʙᴇʀ

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ

x^ɴ + ʏ^ɴ ɪꜱ ᴅɪᴠɪꜱɪʙʟᴇ ʙʏ (x + ʏ) ᴡʜᴇɴ ɴ ɪꜱ ᴏᴅᴅ.

ꜱᴏ,

13^13 + 1 ɪꜱ ᴅɪᴠɪꜱɪʙʟᴇ ʙʏ 13+1 = 14

ꜱᴏ, ɪᴛ ɪꜱ ᴄᴏᴍᴘʟᴇᴛᴇʟʏ ᴅɪᴠɪꜱɪʙʟᴇ ʙʏ 14

ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ

ɪꜰ ᴀ ɴᴜᴍʙᴇʀ ᴇxᴀᴄᴛʟʏ ᴅɪᴠɪꜱɪʙʟᴇ ʙʏ ᴀɴᴏᴛʜᴇʀ ɴᴜᴍʙᴇʀ ᴛʜᴇɴ ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ɪꜱ ᴢᴇʀᴏ.

ꜱᴏ, ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ɪꜱ 0

ᴀɴꜱᴡᴇʀ:-

ᴛʜᴇ ʀᴇᴍᴀɪɴᴅᴇʀ ꜰᴏʀ ᴛʜᴇ ɢɪᴠᴇɴ ᴘʀᴏʙʟᴇᴍ ɪꜱ 0

Answer 2

Answer:

why are you wasting your points?