Question

Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6 Cube + 5 Where Q is some integer

Answer 1

Answer:

1/6

Step-by-step explanation:

6q+1

Q is some integer

6q=-1

q=-1/-6

q=1/6

Answer 2

┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅

ʟᴇᴛ ᴀ ʙᴇ ᴛʜᴇ ᴘᴏsɪᴛɪᴠᴇ ᴏᴅᴅ ɪɴᴛᴇɢᴇʀ ᴡʜɪᴄʜ ᴡʜᴇɴ ᴅɪᴠɪᴅᴇᴅ ʙʏ 6 ɢɪᴠᴇs ϙ ᴀs ϙᴜᴏᴛɪᴇɴᴛ ᴀɴᴅ ʀ ᴀs ʀᴇᴍᴀɪɴᴅᴇʀ.

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴇᴜᴄʟɪᴅ's ᴅɪᴠɪsɪᴏɴ ʟᴇᴍᴍᴀ

ᴀ=ʙϙ+ʀ

ᴀ=6ϙ+ʀ

ᴡʜᴇʀᴇ , ᴀ=0,1,2,3,4,5

ᴛʜᴇɴ,

ᴀ=6ϙ

ᴏʀ

ᴀ=6ϙ+1

ᴏʀ

ᴀ=6ϙ+2

ᴏʀ

ᴀ=6ϙ+3

ᴏʀ

ᴀ=6ϙ+4

ᴏʀ

ᴀ=6ϙ+5

ʙᴜᴛ ʜᴇʀᴇ,

ᴀ=6ϙ+1 & ᴀ=6ϙ+3 & ᴀ=6ϙ+5 ᴀʀᴇ ᴏᴅᴅ.

┅┅┅┅┅┅┅┅┅┅┅┅┅┅┅