I am getting authentication error when I set up gmail account in my alcatel 871a. How can I solve this problem?

there should be an app called playstore on your phone
you need a gmail account www.gmail.com to use playstore
set up an email account
Set this up on the phone when you access playstore and get asked for an email address.
Then search for a browser
http://www.androidauthority.com/best-android-browsers-320252/

Diana, are you hinting you have text messages you don't want your husband to see??

Maybe, try setting-up a second Gmail account, then send transfer) your emails from the old username account to the new username account. If this works, then either try deleting the messages from the old gmail account and transfer the messages from the new gmail account back to the original gmail account ... or ... just delete the old gmail account if you successfully transferred them to the new gmail account.

What do you want?
If you want to unlock your Alcatel OT-871 mobile phone from the network lock,I would suggest you to get an unlock code from http://www.mobile-unlocker.com/alcatel-ot-871/rs5wp9/ at reasonable price.

You may download a copy of the manual at http://www.att.com/support_static_files/manuals/Alcatel_871A.pdf

You might also want to take a look at the video tutorials at http://www.att.com/devicehowto/?make=alcatel&model=871a

Check for a typo in the SMTP server address. You might also try smtp.googlemail.com instead (port 465 SSL). I've seen both used.

the problem should get solved by going to your email account settings (Tools > Account Settings > More Settings), and checking the "My outgoing server (SMTP) requires authentication" option.

The best I can find is that this is related to a malfunctioning cooling fan, I cannot find that specific code for your model, but all other 534 codes from that manufacturer are related to cooling fans

B010/B188 SC 534 Right fusing pressure motor HP error 1 - HP sensor defective
B010/B188 SC 534 Right fusing pressure motor HP error 1 - IOB defective
B010/B188 SC 534 Right fusing pressure motor HP error 1 - Motor defective
B010/B188 SC 534 Right fusing pressure motor HP error 1 - motor drive bound
B132/B200 SC 534 Duplex exhaust fan error - Paper exit fan motor M28 defective, indexed as 146, electrical component layout.
B132/B200 SC 534 Duplex exhaust fan error - check and or replace fusing exhaust fan / paper blocking fan
B132/B200 SC 534 Duplex exhaust fan error - replace duplex fan motors M29 or M30
B222/B224/G878 SC 534 2nd duct fan error - replace fan motor
B230/B237 SC 534 Fusing exit sensor fan error, BICU defective
B230/B237 SC 534 Fusing exit sensor fan error, Fan defective
D014/D015 SC 534 Duplex unit fan error - Fuser exhaust fan blocked or has paper in it.
D014/D015 SC 534 Duplex unit fan error - Duplex Unit fan obstructed
D014/D015 SC 534 Duplex unit fan error - Fan harness disconnected or damaged
D014/D015 SC 534 Duplex unit fan error - Fuser unit connector has paper obstruction
D014/D015 SC 534 Duplex unit fan error - Replace duplex fan
D023/D025 SC 534 Second duct fan error - replace the 2nd duct motor
D023/D025 SC 534 Second duct fan error - replace the IOB
D027/D029 SC 534 Second duct fan error - check connections and harness to fan
D027/D029 SC 534 Second duct fan error - replace fan motor
D037/D038/D041 SC 534 Fusing rear fan error: Check or replace harness
D037/D038/D041 SC 534 Fusing rear fan error: Replace BCU board
D037/D038/D041 SC 534 Fusing rear fan error: Replace fusing rear fan
D037/D038/D041 SC 534 Fusing rear fan error: Replace the DRB

If using Outlook, the problem should get solved by going to your email account settings (Tools > Account Settings > More Settings), and checking the "My outgoing server (SMTP) requires authentication" option.

Then try to send the email.

Hope this helps.